Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
79301	Solve the Differential Equation	y^-1dy+ye^(cos(x))sin(x)dx=0	$y^{- 1} d y + y e^{\cos (x)} \sin (x) d x = 0$
79302	Solve the Differential Equation	(dy)/(dx)=(5x+3)/(y-5) , y(0)=8	$\frac{d y}{d x} = \frac{5 x + 3}{y - 5}$ , $y (0) = 8$
79303	Solve the Differential Equation	(dy)/(dx)=1/(1+y^2)	$\frac{d y}{d x} = \frac{1}{1 + y^{2}}$
79304	Solve the Differential Equation	y''''''''+y''''=2+2x+x^2	$y'''' + y'' = 2 + 2 x + x^{2}$
79305	Solve the Differential Equation	(dy)/(dx)-y^2=1	$\frac{d y}{d x} - y^{2} = 1$
79306	Solve the Differential Equation	(ds)/(dt)=13t(5t^2-1)^3	$\frac{d s}{d t} = 13 t {(5 t^{2} - 1)}^{3}$
79307	Solve the Differential Equation	2(dy)/(dx)=4xe^(-x) , y(0)=5	$2 \frac{d y}{d x} = 4 x e^{- x}$ , $y (0) = 5$
79308	Solve the Differential Equation	(dy)/(dx)=(18-6x^2)/( square root of x^3-9x+2)	$\frac{d y}{d x} = \frac{18 - 6 x^{2}}{\sqrt{x^{3} - 9 x + 2}}$
79309	Solve the Differential Equation	2(12)(5)+2(5)(dy)/(dt)=0	$2 (12) (5) + 2 (5) \frac{d y}{d t} = 0$
79310	Solve the Differential Equation	y''''''''-2y''''+4=0	$y'''' - 2 y'' + 4 = 0$
79311	Solve the Differential Equation	y''''''''=20x^4	$y'''' = 20 x^{4}$
79312	Solve the Differential Equation	xy+(dy)/(dx)=100x	$x y + \frac{d y}{d x} = 100 x$
79313	Solve the Differential Equation	e^(2x)(df)/(dx)+e^x=1	$e^{2 x} \frac{d f}{d x} + e^{x} = 1$
79314	Solve the Differential Equation	xdx+sec(x)sin(ydy)=0	$x d x + \sec (x) \sin (yd y) = 0$
79315	Solve the Differential Equation	y''''+2y''''=2x+5-e^(-2x)	$y'' + 2 y'' = 2 x + 5 - e^{- 2 x}$
79316	Solve the Differential Equation	x(yd)x+(2x^2+y^2)dy=0	$x yd x + (2 x^{2} + y^{2}) d y = 0$
79317	Solve the Differential Equation	(dy)/(dx)=8x^2y-9xy	$\frac{d y}{d x} = 8 x^{2} y - 9 x y$
79318	Solve the Differential Equation	f(x)=x^3(x+9)	$f (x) = x^{3} (x + 9)$
79319	Solve the Differential Equation	t(dx)/(dt)+2x=4e^t	$t \frac{d x}{d t} + 2 x = 4 e^{t}$
79320	Solve the Differential Equation	(ds)/(dt)=t+cos(t) , s(0)=3	$\frac{d s}{d t} = t + \cos (t)$ , $s (0) = 3$
79321	Solve the Differential Equation	(dy)/(dx)=(24-12x^2)/( square root of x^3-6x+4)	$\frac{d y}{d x} = \frac{24 - 12 x^{2}}{\sqrt{x^{3} - 6 x + 4}}$
79322	Solve the Differential Equation	(dy)/(dx)=(3y+4)/(7x+5)	$\frac{d y}{d x} = \frac{3 y + 4}{7 x + 5}$
79323	Solve the Differential Equation	y''''''''+y''''-2y=x	$y'''' + y'' - 2 y = x$
79324	Solve the Differential Equation	2(yd)x+x(x^2 natural log of y-1)dy=0	$2 yd x + x (x^{2} \ln (y) - 1) d y = 0$
79325	Solve the Differential Equation	y^2dx(3xy+y^2-1)dy=0	$y^{2} d x (3 x y + y^{2} - 1) d y = 0$
79326	Solve the Differential Equation	(dy)/(dx)+y=1/(1+e^x)	$\frac{d y}{d x} + y = \frac{1}{1 + e^{x}}$
79327	Solve the Differential Equation	y''''=5e^x+1	$y'' = 5 e^{x} + 1$
79328	Solve the Differential Equation	x(dy)/(dx)-y=x	$x \frac{d y}{d x} - y = x$
79329	Solve the Differential Equation	x^2(dw)/(dx) = square root of w(6x+3)	$x^{2} \frac{d w}{d x} = \sqrt{w} (6 x + 3)$
79330	Solve the Differential Equation	(d^2y)/(dx^2)-2(dy)/(dx)-3y=2sin(x)^2	$\frac{d^{2} y}{d x^{2}} - 2 \frac{d y}{d x} - 3 y = 2 \sin^{2} (x)$
79331	Solve the Differential Equation	(dy)/(dx)=x^2e^(y+2x)	$\frac{d y}{d x} = x^{2} e^{y + 2 x}$
79332	Solve the Differential Equation	(dy)/(dx)=-45x	$\frac{d y}{d x} = - 45 x$
79333	Solve the Differential Equation	y''''''''-y''''-y=0	$y'''' - y'' - y = 0$
79334	Solve the Differential Equation	(ds)/(dt)=-12t+cos(t) , s(0)=4	$\frac{d s}{d t} = - 12 t + \cos (t)$ , $s (0) = 4$
79335	Solve the Differential Equation	sin(y)(x+sin(y))dx+2x^2cos(ydy)=0	$(\sin (y)) (x + \sin (y)) d x + 2 x^{2} \cos (yd y) = 0$
79336	Solve the Differential Equation	y''''''''-y=(2x+1)e^(2x)	$y'''' - y = (2 x + 1) e^{2 x}$
79337	Solve the Differential Equation	x(yd)x+(1+x)(1-y)dy=0	$x yd x + (1 + x) (1 - y) d y = 0$
79338	Solve the Differential Equation	(1+x^2)dy+(1+y^2)dx=0	$(1 + x^{2}) d y + (1 + y^{2}) d x = 0$
79339	Solve the Differential Equation	(dy)/(dx)=y/x+6x+1	$\frac{d y}{d x} = \frac{y}{x} + 6 x + 1$
79340	Solve the Differential Equation	(3x^2+y^2+4)dx+x(x-2y)dy=0	$(3 x^{2} + y^{2} + 4) d x + x (x - 2 y) d y = 0$
79341	Solve the Differential Equation	x(dy)/(dx)-y=x^2cos(2x)	$x \frac{d y}{d x} - y = x^{2} \cos (2 x)$
79342	Solve the Differential Equation	(x+8)y''''=6y	$(x + 8) y'' = 6 y$
79343	Solve the Differential Equation	(df)/(dt)=-2t	$\frac{d f}{d t} = - 2 t$
79344	Solve the Differential Equation	(x+y)^2dx+(x^2+y^2)dy=0	${(x + y)}^{2} d x + (x^{2} + y^{2}) d y = 0$
79345	Solve the Differential Equation	(dy)/(dx)+2y=50	$\frac{d y}{d x} + 2 y = 50$
79346	Solve the Differential Equation	(dy)/(dx)=0.01y(100-y)	$\frac{d y}{d x} = 0.01 y (100 - y)$
79347	Solve the Differential Equation	2y''''''''+y''''=0	$2 y'''' + y'' = 0$
79348	Solve the Differential Equation	(dy)/(dx)=(1+y^2)/(1+x^2)	$\frac{d y}{d x} = \frac{(1 + y^{2})}{(1 + x^{2})}$
79349	Solve the Differential Equation	8xy^3dx+12x^2y^2dy=0	$8 x y^{3} d x + 12 x^{2} y^{2} d y = 0$
79350	Solve the Differential Equation	y''''=y^2sin(x)	$y'' = y^{2} \sin (x)$
79351	Solve the Differential Equation	(sec(x))(dy)/(dx)=e^(y+sin(x)) , y(0)=0	$(\sec (x)) \frac{d y}{d x} = e^{y + \sin (x)}$ , $y (0) = 0$
79352	Solve the Differential Equation	x(dy)/(dx)+2y=x^3-x	$x \frac{d y}{d x} + 2 y = x^{3} - x$
79353	Solve the Differential Equation	(2xy-e^y)dx-(x^2-xe^y)dy=0	$(2 x y - e^{y}) d x - (x^{2} - x e^{y}) d y = 0$
79354	Solve the Differential Equation	(dy)/(dx)=5y+2	$\frac{d y}{d x} = 5 y + 2$
79355	Solve the Differential Equation	y(dy)/(dx)=e^(x+2y)sin(x)	$y \frac{d y}{d x} = e^{x + 2 y} \sin (x)$
79356	Solve the Differential Equation	(dy)/(dx)=(x+y+2)^2	$\frac{d y}{d x} = {(x + y + 2)}^{2}$
79357	Solve the Differential Equation	x^2*(dy)/(dx)=y-xy	$x^{2} \cdot \frac{d y}{d x} = y - x y$
79358	Solve the Differential Equation	y''''''''-4y''''+8=0	$y'''' - 4 y'' + 8 = 0$
79359	Solve the Differential Equation	(dy)/(dx)=1/4 square root of ycos( square root of y)^2	$\frac{d y}{d x} = \frac{1}{4} \sqrt{y} \cos^{2} (\sqrt{y})$
79360	Solve the Differential Equation	e^(5x)(dy)/(dx)+5e^(5x)y=sin(8x)	$e^{5 x} \frac{d y}{d x} + 5 e^{5 x} y = \sin (8 x)$
79361	Solve the Differential Equation	(dy)/(dx)=e^(4x+3y)	$\frac{d y}{d x} = e^{4 x + 3 y}$
79362	Solve the Differential Equation	(y'''')^2-3yy''''+xy=0	${(y'')}^{2} - 3 y y'' + x y = 0$
79363	Solve the Differential Equation	2(7)(0.7)+2(24)(dy)/(dt)=0	$2 (7) (0.7) + 2 (24) \frac{d y}{d t} = 0$
79364	Solve the Differential Equation	x(yd)x=(x+2y)^2dy	$x yd x = {(x + 2 y)}^{2} d y$
79365	Solve the Differential Equation	(dy)/(dx)+6y=0	$\frac{d y}{d x} + 6 y = 0$
79366	Solve the Differential Equation	(dy)/(dx)=7x square root of 2y+20 , y(0)=5	$\frac{d y}{d x} = 7 x \sqrt{2 y + 20}$ , $y (0) = 5$
79367	Solve the Differential Equation	(dy)/(dx)=(11x^2)/( square root of 6+x^3)	$\frac{d y}{d x} = \frac{11 x^{2}}{\sqrt{6 + x^{3}}}$
79368	Solve the Differential Equation	(dy)/(dx)=8+2x-3x^2	$\frac{d y}{d x} = 8 + 2 x - 3 x^{2}$
79369	Solve the Differential Equation	(dy)/(dx)=(5x^4)/(4e^y)	$\frac{d y}{d x} = \frac{5 x^{4}}{4 e^{y}}$
79370	Solve the Differential Equation	(dy)/(dx)=12/((2+3x)^2e^(2y)) , y(-2)=0	$\frac{d y}{d x} = \frac{12}{{(2 + 3 x)}^{2} e^{2 y}}$ , $y (- 2) = 0$
79371	Solve the Differential Equation	y''''+y/(3x)=0	$y'' + \frac{y}{3 x} = 0$
79372	Solve the Differential Equation	x^2(dw)/(dx) = square root of w(8x+1)	$x^{2} \frac{d w}{d x} = \sqrt{w} (8 x + 1)$
79373	Solve the Differential Equation	(dy)/(dt)=8t+6t^2 , y(1)=2	$\frac{d y}{d t} = 8 t + 6 t^{2}$ , $y (1) = 2$
79374	Solve the Differential Equation	(dy)/(dx)=3/(2-x)	$\frac{d y}{d x} = \frac{3}{2 - x}$
79375	Solve the Differential Equation	(dy)/(dx)=-1/(x^2)-3/(x^4)+12	$\frac{d y}{d x} = - \frac{1}{x^{2}} - \frac{3}{x^{4}} + 12$
79376	Solve the Differential Equation	(dx)/(dt)=6xt^2	$\frac{d x}{d t} = 6 x t^{2}$
79377	Solve the Differential Equation	(dy)/(dx)=4x^2y-3xy	$\frac{d y}{d x} = 4 x^{2} y - 3 x y$
79378	Solve the Differential Equation	(dy)/(dx)=(1-y)/(1-x)	$\frac{d y}{d x} = \frac{(1 - y)}{(1 - x)}$
79379	Solve the Differential Equation	xy''''+Ny=5	$x y'' + N y = 5$
79380	Solve the Differential Equation	(dy)/(dx)=7y^-2	$\frac{d y}{d x} = 7 y^{- 2}$
79381	Solve the Differential Equation	y''''=2/x	$y'' = \frac{2}{x}$
79382	Solve the Differential Equation	(dy)/(dx)=7x^2y-8xy	$\frac{d y}{d x} = 7 x^{2} y - 8 x y$
79383	Solve the Differential Equation	(dy)/(dx)=4y^3cos(x)^2	$\frac{d y}{d x} = 4 y^{3} \cos^{2} (x)$
79384	Solve the Differential Equation	(dy)/(dx)-y^2x=x	$\frac{d y}{d x} - y^{2} x = x$
79385	Solve the Differential Equation	(4x^2+2y^2)dx-(xy)dy=0	$(4 x^{2} + 2 y^{2}) d x - (x y) d y = 0$
79386	Solve the Differential Equation	y''''=4xy	$y'' = 4 x y$
79387	Solve the Differential Equation	(dy)/(dx)=0.4y	$\frac{d y}{d x} = 0.4 y$
79388	Solve the Differential Equation	y''''-x^4y^2=y^2	$y'' - x^{4} y^{2} = y^{2}$
79389	Solve the Differential Equation	(dy)/(dx)=9e^x	$\frac{d y}{d x} = 9 e^{x}$
79390	Solve the Differential Equation	(dz)/(dt)=1/(t(t+2))	$\frac{d z}{d t} = \frac{1}{t (t + 2)}$
79391	Solve the Differential Equation	(dy)/(dx)=(7x^2)/( square root of 6+x^3)	$\frac{d y}{d x} = \frac{7 x^{2}}{\sqrt{6 + x^{3}}}$
79392	Solve the Differential Equation	(dy)/(dx)=9x^(1/9)	$\frac{d y}{d x} = 9 x^{\frac{1}{9}}$
79393	Solve the Differential Equation	(dy)/(dx)=3x^2-4x+1	$\frac{d y}{d x} = 3 x^{2} - 4 x + 1$
79394	Solve the Differential Equation	(dp)/(dt)=N(1-N/K)	$\frac{d p}{d t} = N (1 - \frac{N}{K})$
79395	Solve the Differential Equation	(dy)/(dt)=8x^-9	$\frac{d y}{d t} = 8 x^{- 9}$
79396	Solve the Differential Equation	y''''''''''''+3y''''''''+2y''''=0	$y'''''' + 3 y'''' + 2 y'' = 0$
79397	Solve the Differential Equation	(x-2y-1)dx-(x-3)dy=0	$(x - 2 y - 1) d x - (x - 3) d y = 0$
79398	Solve the Differential Equation	6x-10y(dy)/(dx)=0	$6 x - 10 y \frac{d y}{d x} = 0$
79399	Solve the Differential Equation	y'''' = square root of x+y+1	$y'' = \sqrt{x + y + 1}$
79400	Solve the Differential Equation	y''''''''-6y''''+9=0	$y'''' - 6 y'' + 9 = 0$