Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
79001	Solve the Differential Equation	(dy)/(dx)=20-4x-5y+xy	$\frac{d y}{d x} = 20 - 4 x - 5 y + x y$
79002	Solve the Differential Equation	(dR)/(dt)=60/(t^2) , R(1)=20	$\frac{d R}{d t} = \frac{60}{t^{2}}$ , $R (1) = 20$
79003	Solve the Differential Equation	(dy)/(dx)+11/xy=3x^2	$\frac{d y}{d x} + \frac{11}{x} y = 3 x^{2}$
79004	Solve the Differential Equation	(10+x^10)(dy)/(dx)=(x^9)/y	$(10 + x^{10}) \frac{d y}{d x} = \frac{x^{9}}{y}$
79005	Solve the Differential Equation	xdy+(y+2yx^2-2x)dx=0	$x d y + (y + 2 y x^{2} - 2 x) d x = 0$
79006	Solve the Differential Equation	(dy)/(dx)+xsin(2y)=x^3cos(y)^2	$\frac{d y}{d x} + x \sin (2 y) = x^{3} \cos^{2} (y)$
79007	Solve the Differential Equation	(y+1)y''''''''=(y'''')^2	$(y + 1) y'''' = {(y'')}^{2}$
79008	Solve the Differential Equation	(dy)/(dx)=4x natural log of x	$\frac{d y}{d x} = 4 x \ln (x)$
79009	Solve the Differential Equation	3ab''''+b=12a	$3 a b'' + b = 12 a$
79010	Solve the Differential Equation	(dy)/(dt)+4y=11	$\frac{d y}{d t} + 4 y = 11$
79011	Solve the Differential Equation	(dy)/(dx)+1/xy=x^3y^2	$\frac{d y}{d x} + \frac{1}{x} y = x^{3} y^{2}$
79012	Solve the Differential Equation	x((dy)/(dx))=y	$x (\frac{d y}{d x}) = y$
79013	Solve the Differential Equation	xdy-(yd)x=0	$x d y - yd x = 0$
79014	Solve the Differential Equation	y''''=(2x+y)/x	$y'' = \frac{2 x + y}{x}$
79015	Solve the Differential Equation	(dy)/(dx)=2x-2ycot(2x)	$\frac{d y}{d x} = 2 x - 2 y \cot (2 x)$
79016	Solve the Differential Equation	x((dy)/(dx)-y)=x-y	$x (\frac{d y}{d x} - y) = x - y$
79017	Solve the Differential Equation	(dy)/(dx)=6x-5 and y(4)=0	$\frac{d y}{d x} = 6 x - 5$ and $y (4) = 0$
79018	Solve the Differential Equation	(dy)/(dt)=2ty+3y-4t-6	$\frac{d y}{d t} = 2 t y + 3 y - 4 t - 6$
79019	Solve the Differential Equation	sin(ydx)+xcos(ydy)=0	$\sin (yd x) + x \cos (yd y) = 0$
79020	Solve the Differential Equation	(dy)/(dx)=(y(xy-1))/x	$\frac{d y}{d x} = \frac{y (x y - 1)}{x}$
79021	Solve the Differential Equation	(dy)/(dx)=9/(1+x)	$\frac{d y}{d x} = \frac{9}{1 + x}$
79022	Solve the Differential Equation	y''''''''+16y=16tan(4x)	$y'''' + 16 y = 16 \tan (4 x)$
79023	Solve the Differential Equation	(dy)/(dx)+2/xy=8x	$\frac{d y}{d x} + \frac{2}{x} y = 8 x$
79024	Solve the Differential Equation	(x^2+y^2+y)dx+(2xy+x+e^y)dy=0	$(x^{2} + y^{2} + y) d x + (2 x y + x + e^{y}) d y = 0$
79025	Solve the Differential Equation	f(x)=7cos(x)^2	$f (x) = 7 \cos^{2} (x)$
79026	Solve the Differential Equation	(4x^2+3cos(y))dx-xsin(ydy)=0	$(4 x^{2} + 3 \cos (y)) d x - x \sin (yd y) = 0$
79027	Solve the Differential Equation	(dy^2)/(d^2x)-6(dy)/(dx)+9y=2x^2-x+3	$\frac{d y^{2}}{d^{2} x} - 6 \frac{d y}{d x} + 9 y = 2 x^{2} - x + 3$
79028	Solve the Differential Equation	F(x)=(7x+6)^2	$F (x) = {(7 x + 6)}^{2}$
79029	Solve the Differential Equation	xy''''+y=18x	$x y'' + y = 18 x$
79030	Solve the Differential Equation	2yy''''''''=(y'''')^2+1	$2 y y'''' = {(y'')}^{2} + 1$
79031	Solve the Differential Equation	(dy)/(dx)=(xy)/(x+2)	$\frac{d y}{d x} = \frac{x y}{x + 2}$
79032	Solve the Differential Equation	y''''=e^(-y)	$y'' = e^{- y}$
79033	Solve the Differential Equation	(x^2+y^2+2x)dx+2(yd)y=0	$(x^{2} + y^{2} + 2 x) d x + 2 yd y = 0$
79034	Solve the Differential Equation	(dx)/(dt)=x^2+1/64	$\frac{d x}{d t} = x^{2} + \frac{1}{64}$
79035	Solve the Differential Equation	(dy)/(dx)=3/(ycos(x)^2)	$\frac{d y}{d x} = \frac{3}{y \cos^{2} (x)}$
79036	Solve the Differential Equation	f(m)=4m^5-7m^3+m-2	$f (m) = 4 m^{5} - 7 m^{3} + m - 2$
79037	Solve the Differential Equation	(dy)/(dx)=y/x-(y^2)/(x^2)	$\frac{d y}{d x} = \frac{y}{x} - \frac{y^{2}}{x^{2}}$
79038	Solve the Differential Equation	(ye^x+2e^x+y^2)dx+(e^x+2xy)dy=0	$(y e^{x} + 2 e^{x} + y^{2}) d x + (e^{x} + 2 x y) d y = 0$
79039	Solve the Differential Equation	(dy)/(dx)=3x^2 , y(0)=5	$\frac{d y}{d x} = 3 x^{2}$ , $y (0) = 5$
79040	Solve the Differential Equation	(dy)/(dx)=((2-y)^2)/(2 square root of 1+x)	$\frac{d y}{d x} = \frac{{(2 - y)}^{2}}{2 \sqrt{1 + x}}$
79041	Solve the Differential Equation	y''''''''+100y=0	$y'''' + 100 y = 0$
79042	Solve the Differential Equation	x^2y''''+2xy=cos(2x)	$x^{2} y'' + 2 x y = \cos (2 x)$
79043	Solve the Differential Equation	(dy)/(dx)-y=3e^x	$\frac{d y}{d x} - y = 3 e^{x}$
79044	Solve the Differential Equation	(dy)/(dx)=4x^(4/7)	$\frac{d y}{d x} = 4 x^{\frac{4}{7}}$
79045	Solve the Differential Equation	xdy-(yd)x=(x-1)e^xdx	$x d y - yd x = (x - 1) e^{x} d x$
79046	Solve the Differential Equation	(dy)/(dx)=1/(11 square root of x) , y(16)=0	$\frac{d y}{d x} = \frac{1}{11 \sqrt{x}}$ , $y (16) = 0$
79047	Solve the Differential Equation	(dy)/(dx)=(x^2)/(y^2)	$\frac{d y}{d x} = \frac{x^{2}}{y^{2}}$
79048	Solve the Differential Equation	2yy''''''''=1+(y'''')^2	$2 y y'''' = 1 + {(y'')}^{2}$
79049	Solve the Differential Equation	(dx)/(dy)=xye^(y^2)	$\frac{d x}{d y} = x y e^{y^{2}}$
79050	Solve the Differential Equation	(dy)/(dx)=(e^x+4)^2	$\frac{d y}{d x} = {(e^{x} + 4)}^{2}$
79051	Solve the Differential Equation	y''''''''-y=cos(x)	$y'''' - y = \cos (x)$
79052	Solve the Differential Equation	xy''''-y-1=0	$x y'' - y - 1 = 0$
79053	Solve the Differential Equation	y''''=sin(x-y+1)^2	$y'' = \sin^{2} (x - y + 1)$
79054	Solve the Differential Equation	x^2y''''+2xy''''-6y=0	$x^{2} y'' + 2 x y'' - 6 y = 0$
79055	Solve the Differential Equation	y''''-5y''''+6y=2x+3	$y'' - 5 y'' + 6 y = 2 x + 3$
79056	Solve the Differential Equation	(dy)/(dx)=2x^(4/5)	$\frac{d y}{d x} = 2 x^{\frac{4}{5}}$
79057	Solve the Differential Equation	(x-2y)dx+(2y-2x)dy=0	$(x - 2 y) d x + (2 y - 2 x) d y = 0$
79058	Solve the Differential Equation	(dy)/(dx)=(1-y)/x	$\frac{d y}{d x} = \frac{1 - y}{x}$
79059	Solve the Differential Equation	y''''+2x^2y''''+2xy-2x=0	$y'' + 2 x^{2} y'' + 2 x y - 2 x = 0$
79060	Solve the Differential Equation	2x(yd)x+(y^2-x^2)dy=0	$2 x yd x + (y^{2} - x^{2}) d y = 0$
79061	Solve the Differential Equation	xdy+ydx+2xy^2dy=0	$x d y + yd x + 2 x y^{2} d y = 0$
79062	Solve the Differential Equation	(x^3+y^2 square root of y^2+x^2)dx-xy square root of x^2+y^2dy=0	$(x^{3} + y^{2} \sqrt{y^{2} + x^{2}}) d x - x y \sqrt{x^{2} + y^{2}} d y = 0$
79063	Solve the Differential Equation	(dy)/(dx)+y=10	$\frac{d y}{d x} + y = 10$
79064	Solve the Differential Equation	(dy)/(dx)=-y^2+xy+1	$\frac{d y}{d x} = - y^{2} + x y + 1$
79065	Solve the Differential Equation	(dF)/(dx)=4e^x+5x^2 , F(0)=-4	$\frac{d F}{d x} = 4 e^{x} + 5 x^{2}$ , $F (0) = - 4$
79066	Solve the Differential Equation	(d^2y)/(dx^2)-16y=0	$\frac{d^{2} y}{d x^{2}} - 16 y = 0$
79067	Solve the Differential Equation	(dx)/(dt)=e^(x-t)	$\frac{d x}{d t} = e^{x - t}$
79068	Solve the Differential Equation	(dy)/(dx)+4y=2x	$\frac{d y}{d x} + 4 y = 2 x$
79069	Solve the Differential Equation	xy''''+2y=cos(x)	$x y'' + 2 y = \cos (x)$
79070	Solve the Differential Equation	y'''' = square root of y-1	$y'' = \sqrt{y - 1}$
79071	Solve the Differential Equation	(dy)/(dx)=(3x^2+1)/(2y)	$\frac{d y}{d x} = \frac{(3 x^{2} + 1)}{2 y}$
79072	Solve the Differential Equation	(dx)/(dt)=4e^t-2 ; , x(0)=1	$\frac{d x}{d t} = 4 e^{t} - 2$ ; , $x (0) = 1$
79073	Solve the Differential Equation	xcos(xdx)+(1-6y^5)dy=0	$x \cos (x d x) + (1 - 6 y^{5}) d y = 0$
79074	Solve the Differential Equation	1/x(dy)/(dx)-2/(x^2)y=x^2cos(x)	$\frac{1}{x} \cdot \frac{d y}{d x} - \frac{2}{x^{2}} y = x^{2} \cos (x)$
79075	Solve the Differential Equation	y''''''''-2xy''''-2y=0	$y'''' - 2 x y'' - 2 y = 0$
79076	Solve the Differential Equation	(3x^2-2y^2)dy-2x(yd)x=0	$(3 x^{2} - 2 y^{2}) d y - 2 x yd x = 0$
79077	Solve the Differential Equation	(dy)/(dt)=(3t+1)/y	$\frac{d y}{d t} = \frac{3 t + 1}{y}$
79078	Solve the Differential Equation	(d+1)(d+d''''-1)z=sin(2x+3y)	$(d + 1) (d + d'' - 1) z = \sin (2 x + 3 y)$
79079	Solve the Differential Equation	(dy)/(dx)=(y^2)/( square root of x+1)	$\frac{d y}{d x} = \frac{y^{2}}{\sqrt{x + 1}}$
79080	Solve the Differential Equation	(x^2+1)(dy)/(dx)+3x(y-1)=0 , y(0)=9	$(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0$ , $y (0) = 9$
79081	Solve the Differential Equation	(x+2y^3)dx+6xy^2dy=0	$(x + 2 y^{3}) d x + 6 x y^{2} d y = 0$
79082	Solve the Differential Equation	3y(dy)/(dx)=8x^2	$3 y \frac{d y}{d x} = 8 x^{2}$
79083	Solve the Differential Equation	(dy)/(dx)=(x^2e^((-y)/x)+y^2)/(xy)	$\frac{d y}{d x} = \frac{x^{2} e^{\frac{- y}{x}} + y^{2}}{x y}$
79084	Solve the Differential Equation	ty''''(t)-t^2yt=0	$t y'' (t) - t^{2} y t = 0$
79085	Solve the Differential Equation	(dy)/(dx)=x/(10y)	$\frac{d y}{d x} = \frac{x}{10 y}$
79086	Solve the Differential Equation	x^2dy-sin(3xdx)+2x(yd)x=0	$x^{2} d y - \sin (3 x d x) + 2 x yd x = 0$
79087	Solve the Differential Equation	y''''+2y''''+5y=0	$y'' + 2 y'' + 5 y = 0$
79088	Solve the Differential Equation	(dy)/(dx)=1/(9 square root of x) , y(4)=0	$\frac{d y}{d x} = \frac{1}{9 \sqrt{x}}$ , $y (4) = 0$
79089	Solve the Differential Equation	y''''''''''''+y''''''''+y''''+y=0	$y'''''' + y'''' + y'' + y = 0$
79090	Solve the Differential Equation	y''''''''-2ay''''+a^2y=0	$y'''' - 2 a y'' + a^{2} y = 0$
79091	Solve the Differential Equation	f(x)=8x^4	$f (x) = 8 x^{4}$
79092	Solve the Differential Equation	(y-x-10)(dy)/(dx)=x-x	$(y - x - 10) \frac{d y}{d x} = x - x$
79093	Solve the Differential Equation	xy''''''''+2y''''=0	$x y'''' + 2 y'' = 0$
79094	Solve the Differential Equation	y''''-2xy=e^(-x^2)	$y'' - 2 x y = e^{- x^{2}}$
79095	Solve the Differential Equation	(dy)/(dx)=2x-3y , y(0)=1/3	$\frac{d y}{d x} = 2 x - 3 y$ , $y (0) = \frac{1}{3}$
79096	Solve the Differential Equation	(dP)/(dt)=2e^(3t)	$\frac{d P}{d t} = 2 e^{3 t}$
79097	Solve the Differential Equation	(dp)/(dt)=0.2p-10	$\frac{d p}{d t} = 0.2 p - 10$
79098	Solve the Differential Equation	(dy)/(dx)-y/x=1/(x^2)	$\frac{d y}{d x} - \frac{y}{x} = \frac{1}{x^{2}}$
79099	Solve the Differential Equation	(dy)/(dx)=2sec(x)^2(y+3)	$\frac{d y}{d x} = 2 \sec^{2} (x) (y + 3)$
79100	Solve the Differential Equation	y''''=(x^2+xy+y^2)/(x^2)	$y'' = \frac{x^{2} + x y + y^{2}}{x^{2}}$