Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80001	Solve the Differential Equation	(dy)/(dt)=(y+1)/(t(y-1))	$\frac{d y}{d t} = \frac{y + 1}{t (y - 1)}$
80002	Solve the Differential Equation	y''''''''-4y''''-4y=0	$y'''' - 4 y'' - 4 y = 0$
80003	Solve the Differential Equation	2xy^2+4=2(3-x^2y)y''''	$2 x y^{2} + 4 = 2 (3 - x^{2} y) y''$
80004	Solve the Differential Equation	(dy)/(dx)=9x^2y-4xy	$\frac{d y}{d x} = 9 x^{2} y - 4 x y$
80005	Solve the Differential Equation	x^2y''''''''-4y''''=x^4	$x^{2} y'''' - 4 y'' = x^{4}$
80006	Solve the Differential Equation	(d^3y)/(dx^3)-7(dy)/(dx)-6y=0	$\frac{d^{3} y}{d x^{3}} - 7 \frac{d y}{d x} - 6 y = 0$
80007	Solve the Differential Equation	(dy)/(dx)=3x+y^2	$\frac{d y}{d x} = 3 x + y^{2}$
80008	Solve the Differential Equation	y''''=sin(y+x)	$y'' = \sin (y + x)$
80009	Solve the Differential Equation	x(dy)/(dx)=1/y+y	$x \frac{d y}{d x} = \frac{1}{y} + y$
80010	Solve the Differential Equation	y''''''''+4y''''+2.5y=0	$y'''' + 4 y'' + 2.5 y = 0$
80011	Solve the Differential Equation	(dy)/(dx)+y=e^(7x)	$\frac{d y}{d x} + y = e^{7 x}$
80012	Solve the Differential Equation	y''''''''''''+3y''''''''-4y''''=0	$y'''''' + 3 y'''' - 4 y'' = 0$
80013	Solve the Differential Equation	(dy)/(dt)=32t^7	$\frac{d y}{d t} = 32 t^{7}$
80014	Solve the Differential Equation	f(x)=8cos(x)^2	$f (x) = 8 \cos^{2} (x)$
80015	Solve the Differential Equation	(dy)/(dx)=(6x^2)/( square root of 4+x^3)	$\frac{d y}{d x} = \frac{6 x^{2}}{\sqrt{4 + x^{3}}}$
80016	Solve the Differential Equation	(dy)/(dx)=-y(x+1)	$\frac{d y}{d x} = - y (x + 1)$
80017	Solve the Differential Equation	y''''+2y''''+2y=x	$y'' + 2 y'' + 2 y = x$
80018	Solve the Differential Equation	(dy)/(dx)=(7xy)/(( natural log of y)^8)	$\frac{d y}{d x} = \frac{7 x y}{\ln^{8} (y)}$
80019	Solve the Differential Equation	csc(ydx)+sec(xdy)^2=0 ?	$\csc (yd x) + \sec^{2} (x d y) = 0$ ?
80020	Solve the Differential Equation	(d^4y)/(dx^4)+x^2((d^2y)/(dx^2))^3=0	$\frac{d^{4} y}{d x^{4}} + x^{2} {(\frac{d^{2} y}{d x^{2}})}^{3} = 0$
80021	Solve the Differential Equation	y^3y''''+(y^4)/x=x	$y^{3} y'' + \frac{y^{4}}{x} = x$
80022	Solve the Differential Equation	(dy)/(dx)=4y^-2	$\frac{d y}{d x} = 4 y^{- 2}$
80023	Solve the Differential Equation	y''''''''''''-y''''''''-4y''''+4y=5-e^x+e^(2x)	$y'''''' - y'''' - 4 y'' + 4 y = 5 - e^{x} + e^{2 x}$
80024	Solve the Differential Equation	f(x)=\|x-9\|	$f (x) = \| x - 9 \|$
80025	Solve the Differential Equation	(dy)/(dx)=1/2x^3+2/3x^2-4	$\frac{d y}{d x} = \frac{1}{2} x^{3} + \frac{2}{3} x^{2} - 4$
80026	Solve the Differential Equation	(dy)/(dx)+((x-1)^2y)/(x^2(y+1))=0	$\frac{d y}{d x} + \frac{{(x - 1)}^{2} y}{x^{2} (y + 1)} = 0$
80027	Solve the Differential Equation	(dy)/(dx)=xe^(x^2-y)	$\frac{d y}{d x} = x e^{x^{2} - y}$
80028	Solve the Differential Equation	y''''=3y^3+2y+8	$y'' = 3 y^{3} + 2 y + 8$
80029	Solve the Differential Equation	xy''''=y+1	$x y'' = y + 1$
80030	Solve the Differential Equation	x(yd)y-(y^2+3x^2)dx=0	$x yd y - (y^{2} + 3 x^{2}) d x = 0$
80031	Solve the Differential Equation	(dy)/(dx)-5x^2+2=0	$\frac{d y}{d x} - 5 x^{2} + 2 = 0$
80032	Solve the Differential Equation	5y''''=6e^(x/5)+y	$5 y'' = 6 e^{\frac{x}{5}} + y$
80033	Solve the Differential Equation	xy''''=5y	$x y'' = 5 y$
80034	Solve the Differential Equation	(dy)/(dx)=7x^(1/2)	$\frac{d y}{d x} = 7 x^{\frac{1}{2}}$
80035	Solve the Differential Equation	xe^(-t)(dx)/(dy)=t	$x e^{- t} \frac{d x}{d y} = t$
80036	Solve the Differential Equation	(dy)/(dx)=(11x^2)/( square root of 9+x^3)	$\frac{d y}{d x} = \frac{11 x^{2}}{\sqrt{9 + x^{3}}}$
80037	Solve the Differential Equation	(dy)/(dx)-xy=x(1+y)	$\frac{d y}{d x} - x y = x (1 + y)$
80038	Solve the Differential Equation	(dy)/(dx)=x/2	$\frac{d y}{d x} = \frac{x}{2}$
80039	Solve the Differential Equation	y''''=(x+1)^2	$y'' = {(x + 1)}^{2}$
80040	Solve the Differential Equation	xy''''''''+2y''''=8x^2	$x y'''' + 2 y'' = 8 x^{2}$
80041	Solve the Differential Equation	y''''-6y+9y=0	$y'' - 6 y + 9 y = 0$
80042	Solve the Differential Equation	x^2(dy)/(dx)=2xy+6	$x^{2} \frac{d y}{d x} = 2 x y + 6$
80043	Solve the Differential Equation	xy''''+2y=8x^2	$x y'' + 2 y = 8 x^{2}$
80044	Solve the Differential Equation	y''''''''+y''''-6=0	$y'''' + y'' - 6 = 0$
80045	Solve the Differential Equation	(x+2y-3)dy+(2x-y+1)dx=0	$(x + 2 y - 3) d y + (2 x - y + 1) d x = 0$
80046	Solve the Differential Equation	(dy)/(dx)=(y+3)/x when y(3)=3	$\frac{d y}{d x} = \frac{y + 3}{x}$ when $y (3) = 3$
80047	Solve the Differential Equation	f(x)=-C-Dx	$f (x) = - C - D x$
80048	Solve the Differential Equation	(xy^2+3xy)dx-dy=0	$(x y^{2} + 3 x y) d x - d y = 0$
80049	Solve the Differential Equation	(dy)/(dx)-xy^3=0 ; ; , y(2)=4	$\frac{d y}{d x} - x y^{3} = 0$ ; ; , $y (2) = 4$
80050	Solve the Differential Equation	1/36(d^2y)/(dx^2)+(dy)/(dx)+13y=0	$\frac{1}{36} \cdot \frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} + 13 y = 0$
80051	Solve the Differential Equation	(y-x(dy)/(dx))=a(y^2+(dy)/(dx))	$(y - x \frac{d y}{d x}) = a (y^{2} + \frac{d y}{d x})$
80052	Solve the Differential Equation	y''''+x^2y=2x	$y'' + x^{2} y = 2 x$
80053	Solve the Differential Equation	(dy)/(dx)=(9y-8)/(8x-7)	$\frac{d y}{d x} = \frac{9 y - 8}{8 x - 7}$
80054	Solve the Differential Equation	(dy)/(dx)=18x^2-4x	$\frac{d y}{d x} = 18 x^{2} - 4 x$
80055	Solve the Differential Equation	(dy)/(dx)=4x-y	$\frac{d y}{d x} = 4 x - y$
80056	Solve the Differential Equation	y''''=6y^4x^2cos(x^3)	$y'' = 6 y^{4} x^{2} \cos (x^{3})$
80057	Solve the Differential Equation	2(yd)x+e^(-3x)dy=0	$2 yd x + e^{- 3 x} d y = 0$
80058	Solve the Differential Equation	(dy)/(dx)=( square root of 4x-1)/(y^2)	$\frac{d y}{d x} = \frac{\sqrt{4 x - 1}}{y^{2}}$
80059	Solve the Differential Equation	(dy)/(dx)+Py=Q	$\frac{d y}{d x} + P y = Q$
80060	Solve the Differential Equation	(dy)/(dx)=(3sin(pix))/(2y)	$\frac{d y}{d x} = \frac{3 \sin (π x)}{2 y}$
80061	Solve the Differential Equation	y''''''''-7y''''=0	$y'''' - 7 y'' = 0$
80062	Solve the Differential Equation	(dy)/(dx)=x^2-1 , y(3)=7	$\frac{d y}{d x} = x^{2} - 1$ , $y (3) = 7$
80063	Solve the Differential Equation	(dy)/(dx)=(8x^2)/( square root of 9+x^3)	$\frac{d y}{d x} = \frac{8 x^{2}}{\sqrt{9 + x^{3}}}$
80064	Solve the Differential Equation	(dy)/(dx)+2e^(x+y)=0	$\frac{d y}{d x} + 2 e^{x + y} = 0$
80065	Solve the Differential Equation	xy''''-(x+1)y''''+y=0	$x y'' - (x + 1) y'' + y = 0$
80066	Solve the Differential Equation	(e^(x+y))*y''''=x	$(e^{x + y}) \cdot y'' = x$
80067	Solve the Differential Equation	(dy)/(dtheta) = square root of theta-sec(theta)^2	$\frac{d y}{d θ} = \sqrt{θ} - \sec^{2} (θ)$
80068	Solve the Differential Equation	yy''''=Cx	$y y'' = C x$
80069	Solve the Differential Equation	(dy)/(dx)=(x+3y)/(2x)	$\frac{d y}{d x} = \frac{(x + 3 y)}{2 x}$
80070	Solve the Differential Equation	x/(51y^2)=(dy)/(dx)	$\frac{x}{51 y^{2}} = \frac{d y}{d x}$
80071	Solve the Differential Equation	((y-x)(dx)/(dy))x=y	$((y - x) \frac{d x}{d y}) x = y$
80072	Solve the Differential Equation	y''''''''-ay=0	$y'''' - a y = 0$
80073	Solve the Differential Equation	x^5+4y(dy)/(dx)=0	$x^{5} + 4 y \frac{d y}{d x} = 0$
80074	Solve the Differential Equation	(dy)/(dx)=(7e^x-3e^(-x))^2	$\frac{d y}{d x} = {(7 e^{x} - 3 e^{- x})}^{2}$
80075	Solve the Differential Equation	(dy)/(dt)=(1+4t) square root of y	$\frac{d y}{d t} = (1 + 4 t) \sqrt{y}$
80076	Solve the Differential Equation	(dx)/(dt)=-6x+4xy	$\frac{d x}{d t} = - 6 x + 4 x y$
80077	Solve the Differential Equation	x^2dy-1/2y^3dx=0	$x^{2} d y - \frac{1}{2} y^{3} d x = 0$
80078	Solve the Differential Equation	(x^2-1)y''''+2xy=1	$(x^{2} - 1) y'' + 2 x y = 1$
80079	Solve the Differential Equation	y(4+e^x)dy-e^xdx=0	$y (4 + e^{x}) d y - e^{x} d x = 0$
80080	Solve the Differential Equation	y''''=( square root of x)/(7y)	$y'' = \frac{\sqrt{x}}{7 y}$
80081	Solve the Differential Equation	y^2dx-(x+y)^2dy=0	$y^{2} d x - {(x + y)}^{2} d y = 0$
80082	Solve the Differential Equation	(dy)/(dx)+9y=8	$\frac{d y}{d x} + 9 y = 8$
80083	Solve the Differential Equation	(2x+y/x)dx+(4y+ natural log of x)dy=0	$(2 x + \frac{y}{x}) d x + (4 y + \ln (x)) d y = 0$
80084	Solve the Differential Equation	(dy)/(dx)=2x^3 , y(0)=7	$\frac{d y}{d x} = 2 x^{3}$ , $y (0) = 7$
80085	Solve the Differential Equation	(x+y)(yd)x-x^2dy=0	$(x + y) yd x - x^{2} d y = 0$
80086	Solve the Differential Equation	(dy)/(dx)=(y^2-1)/x	$\frac{d y}{d x} = \frac{(y^{2} - 1)}{x}$
80087	Solve the Differential Equation	(2e^y-x)y''''=1	$(2 e^{y} - x) y'' = 1$
80088	Solve the Differential Equation	(dy)/(dx)+y=sin(e^x)	$\frac{d y}{d x} + y = \sin (e^{x})$
80089	Solve the Differential Equation	(dy)/(dx)=20y	$\frac{d y}{d x} = 20 y$
80090	Solve the Differential Equation	(dy)/(dx)=x^2+x-2	$\frac{d y}{d x} = x^{2} + x - 2$
80091	Solve the Differential Equation	(df)/(dx)=4x^2-6e^x , f(0)=-5	$\frac{d f}{d x} = 4 x^{2} - 6 e^{x}$ , $f (0) = - 5$
80092	Solve the Differential Equation	y''''=(3x^2-1)/(3+2y)	$y'' = \frac{3 x^{2} - 1}{3 + 2 y}$
80093	Solve the Differential Equation	(df)/(dx)=45x square root of 9x^2+4 , f(0)=9	$\frac{d f}{d x} = 45 x \sqrt{9 x^{2} + 4}$ , $f (0) = 9$
80094	Solve the Differential Equation	(dy)/(dx)-ysin(2x)-cos(x)=0	$\frac{d y}{d x} - y \sin (2 x) - \cos (x) = 0$
80095	Solve the Differential Equation	(df)/(dx)=12x^5-4x+3 , f(-1)=3	$\frac{d f}{d x} = 12 x^{5} - 4 x + 3$ , $f (- 1) = 3$
80096	Solve the Differential Equation	xy''''+2y''''=0	$x y'' + 2 y'' = 0$
80097	Solve the Differential Equation	f(x)=e^(6x)	$f (x) = e^{6 x}$
80098	Solve the Differential Equation	y''''+y''''+4y=0	$y'' + y'' + 4 y = 0$
80099	Solve the Differential Equation	(dy)/(dt)=(4t^2)/(3y)	$\frac{d y}{d t} = \frac{4 t^{2}}{3 y}$
80100	Solve the Differential Equation	2ye^(y^2)y''''=2x+3 square root of x	$2 y e^{y^{2}} y'' = 2 x + 3 \sqrt{x}$