Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
71401	Solve the Differential Equation	(dy)/(dx)=y-2	$\frac{d y}{d x} = y - 2$
71402	Solve the Differential Equation	(4+e^(2x))dy=ye^(2x)dx	$(4 + e^{2 x}) d y = y e^{2 x} d x$
71403	Solve the Differential Equation	y''''=(x+1)/(y^4+1)	$y'' = \frac{x + 1}{y^{4} + 1}$
71404	Solve the Differential Equation	x(dy)/(dx)=x^2+y	$x \frac{d y}{d x} = x^{2} + y$
71405	Solve the Differential Equation	y''''+2xy=x	$y'' + 2 x y = x$
71406	Solve the Differential Equation	2xy(dy)/(dx)=1+y^2	$2 x y \frac{d y}{d x} = 1 + y^{2}$
71407	Solve the Differential Equation	(dy)/(dx)-y=1/(y^2)	$\frac{d y}{d x} - y = \frac{1}{y^{2}}$
71408	Solve the Differential Equation	(dy)/(dx)=2+ square root of y-2x+3	$\frac{d y}{d x} = 2 + \sqrt{y - 2 x + 3}$
71409	Solve the Differential Equation	(dy)/(dx)=2-y	$\frac{d y}{d x} = 2 - y$
71410	Solve the Differential Equation	(dy)/(dx)=e^(2x+y)	$\frac{d y}{d x} = e^{2 x + y}$
71411	Solve the Differential Equation	(d^2y)/(dx^2)+9y=0	$\frac{d^{2} y}{d x^{2}} + 9 y = 0$
71412	Solve the Differential Equation	y^2dx+x(yd)y=0	$y^{2} d x + x yd y = 0$
71413	Solve the Differential Equation	2(yd)x+(3y-2x)dy=0	$2 yd x + (3 y - 2 x) d y = 0$
71414	Solve the Differential Equation	(dy)/(dx)=-x/y , y(0)=2	$\frac{d y}{d x} = - \frac{x}{y}$ , $y (0) = 2$
71415	Solve the Differential Equation	y''''=1+y^2	$y'' = 1 + y^{2}$
71416	Solve the Differential Equation	y''''''''-2y''''+2y=0	$y'''' - 2 y'' + 2 y = 0$
71417	Solve the Differential Equation	(dy)/(dx)=1+x+y+xy	$\frac{d y}{d x} = 1 + x + y + x y$
71418	Solve the Differential Equation	(dy)/(dx)=6/x	$\frac{d y}{d x} = \frac{6}{x}$
71419	Solve the Differential Equation	y''''''''''''-6y''''''''+11y''''-6y=0	$y'''''' - 6 y'''' + 11 y'' - 6 y = 0$
71420	Solve the Differential Equation	y''''+4y=cos(2t)	$y'' + 4 y = \cos (2 t)$
71421	Solve the Differential Equation	(dy)/(dx)=e^(0.2x)	$\frac{d y}{d x} = e^{0.2 x}$
71422	Solve the Differential Equation	(dy)/(dx)=2/x	$\frac{d y}{d x} = \frac{2}{x}$
71423	Solve the Differential Equation	dx+1/(y^4)dy=0	$d x + \frac{1}{y^{4}} d y = 0$
71424	Solve the Differential Equation	(dy)/(dx)+y/x=x^2	$\frac{d y}{d x} + \frac{y}{x} = x^{2}$
71425	Solve the Differential Equation	(dy)/(dx)=0	$\frac{d y}{d x} = 0$
71426	Solve the Differential Equation	2x(dy)/(dx)=3-x^3	$2 x \frac{d y}{d x} = 3 - x^{3}$
71427	Solve the Differential Equation	(dy)/(dx)=13/x	$\frac{d y}{d x} = \frac{13}{x}$
71428	Solve the Differential Equation	(dy)/(dx)=10y	$\frac{d y}{d x} = 10 y$
71429	Solve the Differential Equation	y^2dt+(2yt+1)dy=0	$y^{2} d t + (2 y t + 1) d y = 0$
71430	Solve the Differential Equation	(2x^2y-2y^2+2xy)dx+(x^2-2y)dy=0	$(2 x^{2} y - 2 y^{2} + 2 x y) d x + (x^{2} - 2 y) d y = 0$
71431	Solve the Differential Equation	(dy)/(dx)=x+5y	$\frac{d y}{d x} = x + 5 y$
71432	Solve the Differential Equation	y''''-x^2y=0	$y'' - x^{2} y = 0$
71433	Solve the Differential Equation	y''''-9y=54	$y'' - 9 y = 54$
71434	Solve the Differential Equation	3y^2(dy)/(dx)=10x	$3 y^{2} \frac{d y}{d x} = 10 x$
71435	Solve the Differential Equation	y''''''''+4y''''+5y=0	$y'''' + 4 y'' + 5 y = 0$
71436	Solve the Differential Equation	(dy)/(dx)=(7x)/y	$\frac{d y}{d x} = \frac{7 x}{y}$
71437	Solve the Differential Equation	(dy)/(dx)=-5y	$\frac{d y}{d x} = - 5 y$
71438	Solve the Differential Equation	xdy+ydx=2x^2(yd)x	$x d y + yd x = 2 x^{2} yd x$
71439	Solve the Differential Equation	(y^2+yx)dx+x^2dy=0	$(y^{2} + y x) d x + x^{2} d y = 0$
71440	Solve the Differential Equation	(du)/(dt)=(1+t^4)/(ut^2+u^4t^2)	$\frac{d u}{d t} = \frac{1 + t^{4}}{u t^{2} + u^{4} t^{2}}$
71441	Solve the Differential Equation	ydx+(2x+3y)dy=0	$yd x + (2 x + 3 y) d y = 0$
71442	Solve the Differential Equation	(dy)/(dx)=5xe^y	$\frac{d y}{d x} = 5 x e^{y}$
71443	Solve the Differential Equation	(dy)/(dx)-2y=x	$\frac{d y}{d x} - 2 y = x$
71444	Solve the Differential Equation	(dy)/(dx)=5/x	$\frac{d y}{d x} = \frac{5}{x}$
71445	Solve the Differential Equation	(dy)/(dx)=x/y , y(0)=-3	$\frac{d y}{d x} = \frac{x}{y}$ , $y (0) = - 3$
71446	Solve the Differential Equation	(dy)/(dx)=7xy	$\frac{d y}{d x} = 7 x y$
71447	Solve the Differential Equation	(x+2y)dx+(2x+y)dy=0	$(x + 2 y) d x + (2 x + y) d y = 0$
71448	Solve the Differential Equation	(x^2+y^2)dx-2x(yd)y=0	$(x^{2} + y^{2}) d x - 2 x yd y = 0$
71449	Solve the Differential Equation	y(4x+y)dx-2(x^2-y)dy=0	$y (4 x + y) d x - 2 (x^{2} - y) d y = 0$
71450	Solve the Differential Equation	x^2y''''=xy+y^2	$x^{2} y'' = x y + y^{2}$
71451	Solve the Differential Equation	y''''=(x^2+1)/(x-1)	$y'' = \frac{x^{2} + 1}{x - 1}$
71452	Solve the Differential Equation	(dy)/(dx)=20x	$\frac{d y}{d x} = 20 x$
71453	Solve the Differential Equation	(x+ye^(y/x))dx-xe^(y/x)dy=0	$(x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0$
71454	Solve the Differential Equation	(dy)/(dx)=tan(x+y)^2	$\frac{d y}{d x} = \tan^{2} (x + y)$
71455	Solve the Differential Equation	(dy)/(dx)=10xy-2x	$\frac{d y}{d x} = 10 x y - 2 x$
71456	Solve the Differential Equation	(x^2+y^2)dx-(xy)dy=0	$(x^{2} + y^{2}) d x - (x y) d y = 0$
71457	Solve the Differential Equation	(dy)/(dx)+y=2+2x	$\frac{d y}{d x} + y = 2 + 2 x$
71458	Solve the Differential Equation	(dy)/(dx) = square root of 1-y^2	$\frac{d y}{d x} = \sqrt{1 - y^{2}}$
71459	Solve the Differential Equation	(dy)/(dx)=y^2-1	$\frac{d y}{d x} = y^{2} - 1$
71460	Solve the Differential Equation	5y^4(dy)/(dx)=12x	$5 y^{4} \frac{d y}{d x} = 12 x$
71461	Solve the Differential Equation	(dy)/(dx)=e^y	$\frac{d y}{d x} = e^{y}$
71462	Solve the Differential Equation	(dy)/(dx)=(y(x+y))/(x^2)	$\frac{d y}{d x} = \frac{y (x + y)}{x^{2}}$
71463	Solve the Differential Equation	y''''=(y-x)/x	$y'' = \frac{y - x}{x}$
71464	Solve the Differential Equation	xdy+ydx=0	$x d y + yd x = 0$
71465	Solve the Differential Equation	(dy)/(dx)-1=2x-1/2	$\frac{d y}{d x} - 1 = 2 x - \frac{1}{2}$
71466	Solve the Differential Equation	(dy)/(dx)=1+y/x	$\frac{d y}{d x} = 1 + \frac{y}{x}$
71467	Solve the Differential Equation	(dy)/(dx)=(x-4)e^(-2y)	$\frac{d y}{d x} = (x - 4) e^{- 2 y}$
71468	Solve the Differential Equation	(dy)/(dx)=-(2x)/y	$\frac{d y}{d x} = - \frac{2 x}{y}$
71469	Solve the Differential Equation	(x^2y-3y)y''''+xy^3=0	$(x^{2} y - 3 y) y'' + x y^{3} = 0$
71470	Solve the Differential Equation	5y^4(dy)/(dx)=2x	$5 y^{4} \frac{d y}{d x} = 2 x$
71471	Solve the Differential Equation	(dy)/(dx)+y=xy^3	$\frac{d y}{d x} + y = x y^{3}$
71472	Solve the Differential Equation	(dy)/(dx)=(sin(x))/(sin(x)+1)	$\frac{d y}{d x} = \frac{\sin (x)}{\sin (x) + 1}$
71473	Solve the Differential Equation	(dy)/(dx)=1/( square root of 4-x^2) , y(0)=pi	$\frac{d y}{d x} = \frac{1}{\sqrt{4 - x^{2}}}$ , $y (0) = π$
71474	Solve the Differential Equation	(dy)/(dx)=(sec(y)^2)/(x^2+1)	$\frac{d y}{d x} = \frac{\sec^{2} (y)}{x^{2} + 1}$
71475	Solve the Differential Equation	(dy)/(dx)=x^2+y^2	$\frac{d y}{d x} = x^{2} + y^{2}$
71476	Solve the Differential Equation	y''''+3x^2y=0	$y'' + 3 x^{2} y = 0$
71477	Solve the Differential Equation	y''''+2y=2e^x	$y'' + 2 y = 2 e^{x}$
71478	Solve the Differential Equation	y''''=2(2x-y)	$y'' = 2 (2 x - y)$
71479	Solve the Differential Equation	cos(x)(dy)/(dx)+y+3=0	$\cos (x) \frac{d y}{d x} + y + 3 = 0$
71480	Solve the Differential Equation	(du)/(dt)=(2+t^4)/(ut^2+u^4t^2)	$\frac{d u}{d t} = \frac{2 + t^{4}}{u t^{2} + u^{4} t^{2}}$
71481	Solve the Differential Equation	(dy)/(dt)=-3y	$\frac{d y}{d t} = - 3 y$
71482	Solve the Differential Equation	(dy)/(dx)=(y^2)/(x^3)	$\frac{d y}{d x} = \frac{y^{2}}{x^{3}}$
71483	Solve the Differential Equation	xy''''+y''''=x	$x y'' + y'' = x$
71484	Solve the Differential Equation	y''''+2xy=0	$y'' + 2 x y = 0$
71485	Solve the Differential Equation	(dy)/(dx)=(x^2)/(10y)-(2x)/(5y)	$\frac{d y}{d x} = \frac{x^{2}}{10 y} - \frac{2 x}{5 y}$
71486	Solve the Differential Equation	(t^2-x)dt-tdx=0	$(t^{2} - x) d t - t d x = 0$
71487	Solve the Differential Equation	(dy)/(dx)=(x-y)/x	$\frac{d y}{d x} = \frac{x - y}{x}$
71488	Solve the Differential Equation	(dy)/(dx)=4x-3	$\frac{d y}{d x} = 4 x - 3$
71489	Solve the Differential Equation	y''''+y/x- square root of y=0	$y'' + \frac{y}{x} - \sqrt{y} = 0$
71490	Solve the Differential Equation	y''''=e^(2x-y)	$y'' = e^{2 x - y}$
71491	Solve the Differential Equation	xy''''=4y	$x y'' = 4 y$
71492	Solve the Differential Equation	x(dy)/(dx)-2y=x^2	$x \frac{d y}{d x} - 2 y = x^{2}$
71493	Solve the Differential Equation	(d^2y)/(dx^2)+(dy)/(dx)=cos(x)	$\frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} = \cos (x)$
71494	Solve the Differential Equation	2x(yd)x+(x^2+3y^2)dy=0	$2 x yd x + (x^{2} + 3 y^{2}) d y = 0$
71495	Solve the Differential Equation	(dy)/(dx)=1/(xy)	$\frac{d y}{d x} = \frac{1}{x y}$
71496	Solve the Differential Equation	(dy)/(dx)=7/x	$\frac{d y}{d x} = \frac{7}{x}$
71497	Solve the Differential Equation	(dy)/(dx)=2x+y	$\frac{d y}{d x} = 2 x + y$
71498	Solve the Differential Equation	(dy)/(dx)+ysec(x)=cos(x)	$\frac{d y}{d x} + y \sec (x) = \cos (x)$
71499	Solve the Differential Equation	(dy)/(dx)=4e^(x-y)	$\frac{d y}{d x} = 4 e^{x - y}$
71500	Solve the Differential Equation	(dy)/(dx)=x/(y^3)	$\frac{d y}{d x} = \frac{x}{y^{3}}$