Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
79701	Solve the Differential Equation	(dy)/(dt)=-2ty+4e^(-t^2) , y(0)=3	$\frac{d y}{d t} = - 2 t y + 4 e^{- t^{2}}$ , $y (0) = 3$
79702	Solve the Differential Equation	y''''+4y''''+4y=2(x+3)	$y'' + 4 y'' + 4 y = 2 (x + 3)$
79703	Solve the Differential Equation	(dy)/(dx)=x^2 square root of x-3	$\frac{d y}{d x} = x^{2} \sqrt{x - 3}$
79704	Solve the Differential Equation	y''''=-6xy	$y'' = - 6 x y$
79705	Solve the Differential Equation	(dy)/(dx)=2e^x+y	$\frac{d y}{d x} = 2 e^{x} + y$
79706	Solve the Differential Equation	ydx-(x- square root of x^2-y^2)dy=0	$yd x - (x - \sqrt{x^{2} - y^{2}}) d y = 0$
79707	Solve the Differential Equation	(dP)/(dt)=P^2-7P+12 , P(0)=1	$\frac{d P}{d t} = P^{2} - 7 P + 12$ , $P (0) = 1$
79708	Solve the Differential Equation	(dy)/(dx)=9x^2+3cos(x) , y(0)=15	$\frac{d y}{d x} = 9 x^{2} + 3 \cos (x)$ , $y (0) = 15$
79709	Solve the Differential Equation	(e^(2x))/(e^(3y))dx+(e^(2y))/(e^(3x))dy=0	$\frac{e^{2 x}}{e^{3 y}} d x + \frac{e^{2 y}}{e^{3 x}} d y = 0$
79710	Solve the Differential Equation	x^4(dy)/(dx)=-y^4	$x^{4} \frac{d y}{d x} = - y^{4}$
79711	Solve the Differential Equation	y''''+2y''''+y=t	$y'' + 2 y'' + y = t$
79712	Solve the Differential Equation	(dy)/(dt)=t^(5/2)y^4	$\frac{d y}{d t} = t^{\frac{5}{2}} y^{4}$
79713	Solve the Differential Equation	(dy)/(dx)=(x^2y-y)/(y+1) , y(3)=1	$\frac{d y}{d x} = \frac{x^{2} y - y}{y + 1}$ , $y (3) = 1$
79714	Solve the Differential Equation	2(12)(0.6)+2(5)(dy)/(dt)=0	$2 (12) (0.6) + 2 (5) \frac{d y}{d t} = 0$
79715	Solve the Differential Equation	(dy)/(dt)=8x^(8/9)	$\frac{d y}{d t} = 8 x^{\frac{8}{9}}$
79716	Solve the Differential Equation	y''''=(-10x-y^2)/(xy)	$y'' = \frac{- 10 x - y^{2}}{x y}$
79717	Solve the Differential Equation	12y''''''''-5y''''-2y=2	$12 y'''' - 5 y'' - 2 y = 2$
79718	Solve the Differential Equation	(dy)/(dt)=(6-y)sin(x)	$\frac{d y}{d t} = (6 - y) \sin (x)$
79719	Solve the Differential Equation	(dy)/(dt)=1/2	$\frac{d y}{d t} = \frac{1}{2}$
79720	Solve the Differential Equation	(dy)/(dx)=2x^4+5x^3+x-4	$\frac{d y}{d x} = 2 x^{4} + 5 x^{3} + x - 4$
79721	Solve the Differential Equation	xy''''+2y=3	$x y'' + 2 y = 3$
79722	Solve the Differential Equation	3yy''''=x	$3 y y'' = x$
79723	Solve the Differential Equation	(dy)/(dx)=(3x^2)/(12y)	$\frac{d y}{d x} = \frac{3 x^{2}}{12 y}$
79724	Solve the Differential Equation	(d^2y)/(dx^2)-5(dy)/(dx)+6y=xe^x	$\frac{d^{2} y}{d x^{2}} - 5 \frac{d y}{d x} + 6 y = x e^{x}$
79725	Solve the Differential Equation	y''''-5y=8	$y'' - 5 y = 8$
79726	Solve the Differential Equation	y''''''''+y=2^x	$y'''' + y = 2^{x}$
79727	Solve the Differential Equation	(dy)/(dx)=4x+7/x	$\frac{d y}{d x} = 4 x + \frac{7}{x}$
79728	Solve the Differential Equation	y''''-2y=e^(3x)	$y'' - 2 y = e^{3 x}$
79729	Solve the Differential Equation	x natural log of xy''''=y	$x \ln (x y'') = y$
79730	Solve the Differential Equation	(2xe^(3y)+e^x)dx+(3x^2e^(3y)-y^2)dy=0	$(2 x e^{3 y} + e^{x}) d x + (3 x^{2} e^{3 y} - y^{2}) d y = 0$
79731	Solve the Differential Equation	y''''''''=6x+4	$y'''' = 6 x + 4$
79732	Solve the Differential Equation	(df)/(dx)=5x square root of 5x^2+4 , f(0)=2	$\frac{d f}{d x} = 5 x \sqrt{5 x^{2} + 4}$ , $f (0) = 2$
79733	Solve the Differential Equation	(dy)/(dx)=7x^-2+5x^-1-1 ; , y(1)=3	$\frac{d y}{d x} = 7 x^{- 2} + 5 x^{- 1} - 1$ ; , $y (1) = 3$
79734	Solve the Differential Equation	3y''''''''-5y''''-6y=12	$3 y'''' - 5 y'' - 6 y = 12$
79735	Solve the Differential Equation	(d^2y)/(dx^2)-4(dy)/(dx)+4y=e^(2x)	$\frac{d^{2} y}{d x^{2}} - 4 \frac{d y}{d x} + 4 y = e^{2 x}$
79736	Solve the Differential Equation	y''''=x/y+y/x+1	$y'' = \frac{x}{y} + \frac{y}{x} + 1$
79737	Solve the Differential Equation	x^4y''''+4x^3y=0	$x^{4} y'' + 4 x^{3} y = 0$
79738	Solve the Differential Equation	x((dy)/(dx))+y=1/(y^2)	$x (\frac{d y}{d x}) + y = \frac{1}{y^{2}}$
79739	Solve the Differential Equation	(dy)/(dt)=yt^2-1.1y	$\frac{d y}{d t} = y t^{2} - 1.1 y$
79740	Solve the Differential Equation	(dy)/(dx)=yx^2+yx	$\frac{d y}{d x} = y x^{2} + y x$
79741	Solve the Differential Equation	e^(-y)dx+(1-xe^(-y))dy=0	$e^{- y} d x + (1 - x e^{- y}) d y = 0$
79742	Solve the Differential Equation	x''''=t/(x-1)	$x'' = \frac{t}{x - 1}$
79743	Solve the Differential Equation	2(24)(0.4)+2(7)(dy)/(dt)=0	$2 (24) (0.4) + 2 (7) \frac{d y}{d t} = 0$
79744	Solve the Differential Equation	(d^2y)/(dx^2)+4(dy)/(dx)+9y=0	$\frac{d^{2} y}{d x^{2}} + 4 \frac{d y}{d x} + 9 y = 0$
79745	Solve the Differential Equation	y''''=12x-4	$y'' = 12 x - 4$
79746	Solve the Differential Equation	(x^2e^(-y/x)+y^2)dx=x(yd)y	$(x^{2} e^{- \frac{y}{x}} + y^{2}) d x = x yd y$
79747	Solve the Differential Equation	(dy)/(dx)=6xy-5x	$\frac{d y}{d x} = 6 x y - 5 x$
79748	Solve the Differential Equation	y''''''''-y''''=e^xcos(x)	$y'''' - y'' = e^{x} \cos (x)$
79749	Solve the Differential Equation	(dc)/(dx)=1/(2 square root of x)	$\frac{d c}{d x} = \frac{1}{2 \sqrt{x}}$
79750	Solve the Differential Equation	(15x^2y^2-y^4)dx+(10x^3y-4xy^3-5y^4)dy=0	$(15 x^{2} y^{2} - y^{4}) d x + (10 x^{3} y - 4 x y^{3} - 5 y^{4}) d y = 0$
79751	Solve the Differential Equation	xdx+sec(x)sin(y)dy=0	$x d x + \sec (x) \sin (y) d y = 0$
79752	Solve the Differential Equation	(dy)/(dx)=e^(3x-3y)	$\frac{d y}{d x} = e^{3 x - 3 y}$
79753	Solve the Differential Equation	(dy)/(dx)=2y+2	$\frac{d y}{d x} = 2 y + 2$
79754	Solve the Differential Equation	xy''''+xy+y=e^(-x)	$x y'' + x y + y = e^{- x}$
79755	Solve the Differential Equation	dy=6xdx-2yxdx	$d y = 6 x d x - 2 y x d x$
79756	Solve the Differential Equation	(3x^2y^4+2xy)dx+(2x^3y^3-x^2)dy=0	$(3 x^{2} y^{4} + 2 x y) d x + (2 x^{3} y^{3} - x^{2}) d y = 0$
79757	Solve the Differential Equation	y''''+y=2sin(x)	$y'' + y = 2 \sin (x)$
79758	Solve the Differential Equation	(ds)/(dt)=7t(4t^2-7)^3	$\frac{d s}{d t} = 7 t {(4 t^{2} - 7)}^{3}$
79759	Solve the Differential Equation	(dy)/(dt)=(8t^2)/(9y)	$\frac{d y}{d t} = \frac{8 t^{2}}{9 y}$
79760	Solve the Differential Equation	(dy)/(dx)=8x^(4/9)	$\frac{d y}{d x} = 8 x^{\frac{4}{9}}$
79761	Solve the Differential Equation	(dy)/(dx)+sec(xy)=cos(x)	$\frac{d y}{d x} + \sec (x y) = \cos (x)$
79762	Solve the Differential Equation	(x+y-4)dx-(3x-y-4)dy=0	$(x + y - 4) d x - (3 x - y - 4) d y = 0$
79763	Solve the Differential Equation	3xdy-4(yd)x=0	$3 x d y - 4 yd x = 0$
79764	Solve the Differential Equation	(dv)/(dt)=3/(t square root of t^2-1) , v(2)=0	$\frac{d v}{d t} = \frac{3}{t \sqrt{t^{2} - 1}}$ , $v (2) = 0$
79765	Solve the Differential Equation	(dy)/(dx)=(x^2+y^2)/(xy-x^2)	$\frac{d y}{d x} = \frac{x^{2} + y^{2}}{x y - x^{2}}$
79766	Solve the Differential Equation	(dP)/(dt)=P	$\frac{d P}{d t} = P$
79767	Solve the Differential Equation	(2y-3x)dx+xdy=0	$(2 y - 3 x) d x + x d y = 0$
79768	Solve the Differential Equation	1+e^(-3x)y''''=0	$1 + e^{- 3 x} y'' = 0$
79769	Solve the Differential Equation	y''''=3(2+y)x^2	$y'' = 3 (2 + y) x^{2}$
79770	Solve the Differential Equation	(ds)/(dt)=-7t+cos(t) , s(0)=-5	$\frac{d s}{d t} = - 7 t + \cos (t)$ , $s (0) = - 5$
79771	Solve the Differential Equation	(dx)/(dy)-y=e^xy^2	$\frac{d x}{d y} - y = e^{x} y^{2}$
79772	Solve the Differential Equation	x^2*y''''+y=0	$x^{2} \cdot y'' + y = 0$
79773	Solve the Differential Equation	(dy)/(dx)=5+x	$\frac{d y}{d x} = 5 + x$
79774	Solve the Differential Equation	(dx)/(dt)=y	$\frac{d x}{d t} = y$
79775	Solve the Differential Equation	(3x^2+6xy^2)dx+(6x^2y+4y^2)dy=0	$(3 x^{2} + 6 x y^{2}) d x + (6 x^{2} y + 4 y^{2}) d y = 0$
79776	Solve the Differential Equation	(dy)/(dt)=3/4y	$\frac{d y}{d t} = \frac{3}{4} y$
79777	Solve the Differential Equation	(dx)/(dt)=9/x , x(0)=9	$\frac{d x}{d t} = \frac{9}{x}$ , $x (0) = 9$
79778	Solve the Differential Equation	(df)/(dx)=1/(x^2f^2+1)	$\frac{d f}{d x} = \frac{1}{x^{2} f^{2} + 1}$
79779	Solve the Differential Equation	(dy)/(dx)=(10x^2)/( square root of 6+x^3)	$\frac{d y}{d x} = \frac{10 x^{2}}{\sqrt{6 + x^{3}}}$
79780	Solve the Differential Equation	xsin(ydx)^2+cot(ydy)=0	$x \sin^{2} (yd x) + \cot (yd y) = 0$
79781	Solve the Differential Equation	(dy)/(dx)=2x square root of 4-y^2	$\frac{d y}{d x} = 2 x \sqrt{4 - y^{2}}$
79782	Solve the Differential Equation	y''''''''+1=0	$y'''' + 1 = 0$
79783	Solve the Differential Equation	(x^2+xy-y^2)dx+x(yd)y=0	$(x^{2} + x y - y^{2}) d x + x yd y = 0$
79784	Solve the Differential Equation	x^7+14y(dy)/(dx)=0	$x^{7} + 14 y \frac{d y}{d x} = 0$
79785	Solve the Differential Equation	(x^2+3)(dy)/(dx)-x=0	$(x^{2} + 3) \frac{d y}{d x} - x = 0$
79786	Solve the Differential Equation	y''''''''+4y''''+4y=-5sin(x)+10cos(x)	$y'''' + 4 y'' + 4 y = - 5 \sin (x) + 10 \cos (x)$
79787	Solve the Differential Equation	y''''=6x^2-8x+1	$y'' = 6 x^{2} - 8 x + 1$
79788	Solve the Differential Equation	y''''''''-4y''''+4y=e^x	$y'''' - 4 y'' + 4 y = e^{x}$
79789	Solve the Differential Equation	(dy)/(dx)=(7y^2)/( square root of x)	$\frac{d y}{d x} = \frac{7 y^{2}}{\sqrt{x}}$
79790	Solve the Differential Equation	f(x)=7x	$f (x) = 7 x$
79791	Solve the Differential Equation	9yy''''+4x=0	$9 y y'' + 4 x = 0$
79792	Solve the Differential Equation	y''''=8x-4	$y'' = 8 x - 4$
79793	Solve the Differential Equation	y''''''''+4y=3-sin(2x)	$y'''' + 4 y = 3 - \sin (2 x)$
79794	Solve the Differential Equation	y''''=(x^2)/(1+y^2)	$y'' = \frac{x^{2}}{1 + y^{2}}$
79795	Solve the Differential Equation	(df)/(dx)=35x square root of 5x^2+4 , f(0)=15	$\frac{d f}{d x} = 35 x \sqrt{5 x^{2} + 4}$ , $f (0) = 15$
79796	Solve the Differential Equation	4x+(dy)/(dx)=36x^5+12	$4 x + \frac{d y}{d x} = 36 x^{5} + 12$
79797	Solve the Differential Equation	y''''-3y''''+3y=0	$y'' - 3 y'' + 3 y = 0$
79798	Solve the Differential Equation	2x^2y''''''''+3xy''''=y	$2 x^{2} y'''' + 3 x y'' = y$
79799	Solve the Differential Equation	(dy)/(dx)=(5+y^3)/2	$\frac{d y}{d x} = \frac{(5 + y^{3})}{2}$
79800	Solve the Differential Equation	(dy)/(dx)=10x^5	$\frac{d y}{d x} = 10 x^{5}$