Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72501	Solve the Differential Equation	(y^3+kxy^4-2x)dx+(3xy^2+20x^2y^3)dy=0	$(y^{3} + k x y^{4} - 2 x) d x + (3 x y^{2} + 20 x^{2} y^{3}) d y = 0$
72502	Solve the Differential Equation	(dy)/(dx)=8x^3-3x^2+x	$\frac{d y}{d x} = 8 x^{3} - 3 x^{2} + x$
72503	Solve the Differential Equation	y''''+3y=2x	$y'' + 3 y = 2 x$
72504	Solve the Differential Equation	(dy)/(dx)=-8x+9x^2	$\frac{d y}{d x} = - 8 x + 9 x^{2}$
72505	Solve the Differential Equation	y''''+y^2sin(x)=0	$y'' + y^{2} \sin (x) = 0$
72506	Solve the Differential Equation	y''''''''+18y+18=3x^2+1	$y'''' + 18 y + 18 = 3 x^{2} + 1$
72507	Solve the Differential Equation	(dy)/(dx)=(10x)/(e^y)	$\frac{d y}{d x} = \frac{10 x}{e^{y}}$
72508	Solve the Differential Equation	2yxdx+x^2dy=0	$2 y x d x + x^{2} d y = 0$
72509	Solve the Differential Equation	dx-(1+2xtan(y))dy=0	$d x - (1 + 2 x \tan (y)) d y = 0$
72510	Solve the Differential Equation	(dy)/(dx)=(-y^2)/x	$\frac{d y}{d x} = \frac{- y^{2}}{x}$
72511	Solve the Differential Equation	(dy)/(dx)=5y^2	$\frac{d y}{d x} = 5 y^{2}$
72512	Solve the Differential Equation	t(s^2+t^2)ds-s(s^2-t^2)dt=0	$t (s^{2} + t^{2}) d s - s (s^{2} - t^{2}) d t = 0$
72513	Solve the Differential Equation	(dy)/(dx)=(4x^2+7xy+2y^2)/(x^2)	$\frac{d y}{d x} = \frac{4 x^{2} + 7 x y + 2 y^{2}}{x^{2}}$
72514	Solve the Differential Equation	x''''''''+x=0	$x'''' + x = 0$
72515	Solve the Differential Equation	(t^2+x^2)dt+(2tx-x)dx=0	$(t^{2} + x^{2}) d t + (2 t x - x) d x = 0$
72516	Solve the Differential Equation	y(d^2x)/(dy^2)=y^2+1	$y \frac{d^{2} x}{d y^{2}} = y^{2} + 1$
72517	Solve the Differential Equation	(x^2-y)dx-xdy=0	$(x^{2} - y) d x - x d y = 0$
72518	Solve the Differential Equation	(dy)/(dt)=3t^2	$\frac{d y}{d t} = 3 t^{2}$
72519	Solve the Differential Equation	y''''+xy=6xy^(1/2)	$y'' + x y = 6 x y^{\frac{1}{2}}$
72520	Solve the Differential Equation	(dy)/(dx)=(4-2x)/(3y^2-5)	$\frac{d y}{d x} = \frac{4 - 2 x}{3 y^{2} - 5}$
72521	Solve the Differential Equation	(dy)/(dx)=-4x+6x^2	$\frac{d y}{d x} = - 4 x + 6 x^{2}$
72522	Solve the Differential Equation	y''''=y+2	$y'' = y + 2$
72523	Solve the Differential Equation	(dy)/(dx)=-(sin(x+5))/y	$\frac{d y}{d x} = - \frac{\sin (x + 5)}{y}$
72524	Solve the Differential Equation	(dy)/(dx)=(6y)/x	$\frac{d y}{d x} = \frac{6 y}{x}$
72525	Solve the Differential Equation	(dy)/(dx)=-4xy^2	$\frac{d y}{d x} = - 4 x y^{2}$
72526	Solve the Differential Equation	16x-6y''''=0	$16 x - 6 y'' = 0$
72527	Solve the Differential Equation	y''''''''+6y''''+13y=0	$y'''' + 6 y'' + 13 y = 0$
72528	Solve the Differential Equation	xe^ydy+(x^2-1)/ydx=0	$x e^{y} d y + \frac{x^{2} - 1}{y} d x = 0$
72529	Solve the Differential Equation	(dy)/(dx)=xy+x-2y-2	$\frac{d y}{d x} = x y + x - 2 y - 2$
72530	Solve the Differential Equation	1/x(dy)/(dx)=e^y	$\frac{1}{x} \cdot \frac{d y}{d x} = e^{y}$
72531	Solve the Differential Equation	(3x^2y-4xy^3+6x)dx+(x^3-6x^2y^2-1)dy=0	$(3 x^{2} y - 4 x y^{3} + 6 x) d x + (x^{3} - 6 x^{2} y^{2} - 1) d y = 0$
72532	Solve the Differential Equation	(dy)/(dx)=e^y(3x^2-6x)	$\frac{d y}{d x} = e^{y} (3 x^{2} - 6 x)$
72533	Solve the Differential Equation	y''''-xy=0	$y'' - x y = 0$
72534	Solve the Differential Equation	(dy)/(dx)=(4x)/(e^y)	$\frac{d y}{d x} = \frac{4 x}{e^{y}}$
72535	Solve the Differential Equation	(dy)/(dx)=(3e^x)/(e^y)	$\frac{d y}{d x} = \frac{3 e^{x}}{e^{y}}$
72536	Solve the Differential Equation	(1+x^2+y^2+x^2y^2)dy=(1+y^2)dx	$(1 + x^{2} + y^{2} + x^{2} y^{2}) d y = (1 + y^{2}) d x$
72537	Solve the Differential Equation	(e^x+y)dx+(e^y+x)dy=0	$(e^{x} + y) d x + (e^{y} + x) d y = 0$
72538	Solve the Differential Equation	(dy)/(dx)=(x-4)/( square root of x^2-8x+1)	$\frac{d y}{d x} = \frac{x - 4}{\sqrt{x^{2} - 8 x + 1}}$
72539	Solve the Differential Equation	(x^2+y^2+x)dx+x(yd)y=0	$(x^{2} + y^{2} + x) d x + x yd y = 0$
72540	Solve the Differential Equation	(dy)/(dx)=(xcos(x^2))/(4y)	$\frac{d y}{d x} = \frac{x \cos (x^{2})}{4 y}$
72541	Solve the Differential Equation	2(dy)/(dtheta)=(e^ysin(theta)^2)/(ysec(theta))	$2 \frac{d y}{d θ} = \frac{e^{y} \sin^{2} (θ)}{y \sec (θ)}$
72542	Solve the Differential Equation	x^2(dy)/(dx)=3x^2-xy	$x^{2} \frac{d y}{d x} = 3 x^{2} - x y$
72543	Solve the Differential Equation	e^(-y)cos(x)-(dy)/(dx)=0	$e^{- y} \cos (x) - \frac{d y}{d x} = 0$
72544	Solve the Differential Equation	xy''''=e^y+2y''''	$x y'' = e^{y} + 2 y''$
72545	Solve the Differential Equation	(2y^2+2y+4x^2)dx+(2xy+x)dy=0	$(2 y^{2} + 2 y + 4 x^{2}) d x + (2 x y + x) d y = 0$
72546	Solve the Differential Equation	(1+y^2)dx+xydy=0	$(1 + y^{2}) \cdot d x + x y \cdot d y = 0$
72547	Solve the Differential Equation	nx(dy)/(dx)+2y=xy^(n+1)	$n x \frac{d y}{d x} + 2 y = x y^{n + 1}$
72548	Solve the Differential Equation	2x(dy)/(dx)-y=3	$2 x \frac{d y}{d x} - y = 3$
72549	Solve the Differential Equation	y''''+6y=0	$y'' + 6 y = 0$
72550	Solve the Differential Equation	(ds)/(dt)=20t(5t^2-3)^3 , s(1)=15	$\frac{d s}{d t} = 20 t {(5 t^{2} - 3)}^{3}$ , $s (1) = 15$
72551	Solve the Differential Equation	(dy)/(dx)=44x	$\frac{d y}{d x} = 44 x$
72552	Solve the Differential Equation	(dr)/(dtheta)=-picos(pitheta) , r(0)=3	$\frac{d r}{d θ} = - π \cos (π θ)$ , $r (0) = 3$
72553	Solve the Differential Equation	y''''=1+4y^2	$y'' = 1 + 4 y^{2}$
72554	Solve the Differential Equation	(3y/x-8)dx+3dy=0	$(3 \frac{y}{x} - 8) d x + 3 d y = 0$
72555	Solve the Differential Equation	(dy)/(dx)=(x-1)/(3y^2)	$\frac{d y}{d x} = \frac{x - 1}{3 y^{2}}$
72556	Solve the Differential Equation	y''''''''+4y''''+13y=0	$y'''' + 4 y'' + 13 y = 0$
72557	Solve the Differential Equation	y''''''''''''-8y=0	$y'''''' - 8 y = 0$
72558	Solve the Differential Equation	(dy)/(dx)=5x^3+3x	$\frac{d y}{d x} = 5 x^{3} + 3 x$
72559	Solve the Differential Equation	(2x-y)dx+(2y-x)dy=0	$(2 x - y) d x + (2 y - x) d y = 0$
72560	Solve the Differential Equation	x+y(dy)/(dx)=0	$x + y \frac{d y}{d x} = 0$
72561	Solve the Differential Equation	x(yd)x+(x+1)dy=0	$x yd x + (x + 1) d y = 0$
72562	Solve the Differential Equation	(2xy+2y)dx-(yd)y=0	$(2 x y + 2 y) d x - yd y = 0$
72563	Solve the Differential Equation	(y^2+xy)dx+x^2dy=0	$(y^{2} + x y) d x + x^{2} d y = 0$
72564	Solve the Differential Equation	(dy)/(dx)=sin(x)+cos(x)	$\frac{d y}{d x} = \sin (x) + \cos (x)$
72565	Solve the Differential Equation	(dy)/(dx)=(x-2y)/x	$\frac{d y}{d x} = \frac{x - 2 y}{x}$
72566	Solve the Differential Equation	(dr)/(dtheta)=-pisin(pitheta) , r(1)=2	$\frac{d r}{d θ} = - π \sin (π θ)$ , $r (1) = 2$
72567	Solve the Differential Equation	(dx)/y-(xdy)/(y^2)=0	$\frac{d x}{y} - \frac{x d y}{y^{2}} = 0$
72568	Solve the Differential Equation	(dy)/(dx)+y=xy^4	$\frac{d y}{d x} + y = x y^{4}$
72569	Solve the Differential Equation	2x^3(yd)x+(x^4+y^4)dy=0	$2 x^{3} yd x + (x^{4} + y^{4}) d y = 0$
72570	Solve the Differential Equation	(y^4-3x^2)dy=-x(yd)x	$(y^{4} - 3 x^{2}) d y = - x yd x$
72571	Solve the Differential Equation	x(dy)/(dx)+(2x+1)/(x+1)y=x-1	$x \frac{d y}{d x} + \frac{2 x + 1}{x + 1} y = x - 1$
72572	Solve the Differential Equation	(dy)/(dx)+x^2y=x+1	$\frac{d y}{d x} + x^{2} y = x + 1$
72573	Solve the Differential Equation	(dr)/(ds)=0.2r	$\frac{d r}{d s} = 0.2 r$
72574	Solve the Differential Equation	(xy^2+x)dx+(x^2y-y)dy=0	$(x y^{2} + x) d x + (x^{2} y - y) d y = 0$
72575	Solve the Differential Equation	(2y-x+3)dx+2dy=0	$(2 y - x + 3) d x + 2 d y = 0$
72576	Solve the Differential Equation	tan(ydy)^2=sin(xdx)^3	$\tan^{2} (yd y) = \sin^{3} (x d x)$
72577	Solve the Differential Equation	(6xy-2y^2+1)dx+(3x^2-4xy)dy=0	$(6 x y - 2 y^{2} + 1) d x + (3 x^{2} - 4 x y) d y = 0$
72578	Solve the Differential Equation	(dy)/(dx)=y^3cos(x)	$\frac{d y}{d x} = y^{3} \cos (x)$
72579	Solve the Differential Equation	y''''-y''''=x^2+e^x	$y'' - y'' = x^{2} + e^{x}$
72580	Solve the Differential Equation	(dy)/(dx)=(x+y)/x : y(1)=1	$\frac{d y}{d x} = \frac{x + y}{x}$ : $y (1) = 1$
72581	Solve the Differential Equation	(x-y)dx-(x+y)dy=0	$(x - y) d x - (x + y) d y = 0$
72582	Solve the Differential Equation	(3y^2+10xy^2)dx+(6xy-2+10x^2y)dy=0	$(3 y^{2} + 10 x y^{2}) d x + (6 x y - 2 + 10 x^{2} y) d y = 0$
72583	Solve the Differential Equation	(2x+3)y''''=(y+2x+3)^(1/2)	$(2 x + 3) y'' = {(y + 2 x + 3)}^{\frac{1}{2}}$
72584	Solve the Differential Equation	(1+2y)dx+(4-x^2)dy=0	$(1 + 2 y) d x + (4 - x^{2}) d y = 0$
72585	Solve the Differential Equation	(dy)/(dx)=5xy^2	$\frac{d y}{d x} = 5 x y^{2}$
72586	Solve the Differential Equation	(dy)/(dx)=((2-y)^2)/(2(1+x)^(1/2))	$\frac{d y}{d x} = \frac{{(2 - y)}^{2}}{2 {(1 + x)}^{\frac{1}{2}}}$
72587	Solve the Differential Equation	ydx=(x- square root of xy)dy	$yd x = (x - \sqrt{x y}) d y$
72588	Solve the Differential Equation	(dx)/(dt)=x/2	$\frac{d x}{d t} = \frac{x}{2}$
72589	Solve the Differential Equation	(dy)/(dx)=(y-x)/x	$\frac{d y}{d x} = \frac{y - x}{x}$
72590	Solve the Differential Equation	(x^2-y^2)dx+x(yd)y=0	$(x^{2} - y^{2}) d x + x yd y = 0$
72591	Solve the Differential Equation	(dy)/(dx)=ysin(x)^3	$\frac{d y}{d x} = y \sin^{3} (x)$
72592	Solve the Differential Equation	(dy)/(dx)=(x^2+4)/(-3y^2)	$\frac{d y}{d x} = \frac{x^{2} + 4}{- 3 y^{2}}$
72593	Solve the Differential Equation	(dy)/(dx)=10e^(-2x)	$\frac{d y}{d x} = 10 e^{- 2 x}$
72594	Solve the Differential Equation	2(dy)/(dx)+4y=6x	$2 \frac{d y}{d x} + 4 y = 6 x$
72595	Solve the Differential Equation	y''''+3x^2y=6x^2	$y'' + 3 x^{2} y = 6 x^{2}$
72596	Solve the Differential Equation	y''''-16y=0	$y'' - 16 y = 0$
72597	Solve the Differential Equation	(x-4y-9)dx+(4x+y-2)dy=0	$(x - 4 y - 9) d x + (4 x + y - 2) d y = 0$
72598	Solve the Differential Equation	(dy)/(dx)=x-3	$\frac{d y}{d x} = x - 3$
72599	Solve the Differential Equation	(dy)/(dx)=-4x+3x^2	$\frac{d y}{d x} = - 4 x + 3 x^{2}$
72600	Solve the Differential Equation	(2x^3-xy^2-2y+3)dx+(x^(2y)+2x)dy=0	$(2 x^{3} - x y^{2} - 2 y + 3) d x + (x^{2 y} + 2 x) d y = 0$