Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
71501	Solve the Differential Equation	6x(yd)x+(4y+9x^2)dy=0	$6 x yd x + (4 y + 9 x^{2}) d y = 0$
71502	Solve the Differential Equation	(dy)/(dx)=2ycos(x)	$\frac{d y}{d x} = 2 y \cos (x)$
71503	Solve the Differential Equation	y''''-2/xy=0	$y'' - \frac{2}{x} y = 0$
71504	Solve the Differential Equation	x(dy)/(dx)-y=x^2sin(x)	$x \frac{d y}{d x} - y = x^{2} \sin (x)$
71505	Solve the Differential Equation	(dy)/(dx)+y=yxe^(x+2)	$\frac{d y}{d x} + y = y x e^{x + 2}$
71506	Solve the Differential Equation	x(yd)y=y^2dx+ydy	$x yd y = y^{2} d x + yd y$
71507	Solve the Differential Equation	(dy)/(dx)+2/xy=x	$\frac{d y}{d x} + \frac{2}{x} y = x$
71508	Solve the Differential Equation	(dy)/(dx)=11y	$\frac{d y}{d x} = 11 y$
71509	Solve the Differential Equation	( square root of 1+x^2)/(1+y)(dy)/(dx)=2x	$\frac{\sqrt{1 + x^{2}}}{1 + y} \cdot \frac{d y}{d x} = 2 x$
71510	Verify the Existence and Uniqueness of Solutions for the Differential Equation	(dy)/(dx)=2x^3y , (1,1)	$\frac{d y}{d x} = 2 x^{3} y$ , $(1, 1)$
71511	Solve the Differential Equation	y''''-yx=x	$y'' - y x = x$
71512	Solve the Differential Equation	(2x-3y)dx+(2y-3x)dy=0	$(2 x - 3 y) d x + (2 y - 3 x) d y = 0$
71513	Solve the Differential Equation	(dy)/(dx)=1/(3y^2)	$\frac{d y}{d x} = \frac{1}{3 y^{2}}$
71514	Solve the Differential Equation	y''''+y=y^2e^x	$y'' + y = y^{2} e^{x}$
71515	Solve the Differential Equation	(dx)/(dt)=x/t	$\frac{d x}{d t} = \frac{x}{t}$
71516	Solve the Differential Equation	(dx)/(dt)=4(x^2+1)	$\frac{d x}{d t} = 4 (x^{2} + 1)$
71517	Solve the Differential Equation	(x+y)^2dx+(2xy+x^2-1)dy=0	${(x + y)}^{2} d x + (2 x y + x^{2} - 1) d y = 0$
71518	Solve the Differential Equation	(3xy+y^2)dx+(x^2+xy)dy=0	$(3 x y + y^{2}) d x + (x^{2} + x y) d y = 0$
71519	Solve the Differential Equation	(2y^2x-3)dx+(2yx^2+4)dy=0	$(2 y^{2} x - 3) d x + (2 y x^{2} + 4) d y = 0$
71520	Solve the Differential Equation	(dy)/(dx)+y=1	$\frac{d y}{d x} + y = 1$
71521	Solve the Differential Equation	(x+1)(dy)/(dx)=x+6	$(x + 1) \frac{d y}{d x} = x + 6$
71522	Solve the Differential Equation	(dy)/(dx)=-1/(5xy)	$\frac{d y}{d x} = - \frac{1}{5 x y}$
71523	Solve the Differential Equation	(dy)/(dx)=(3x)/y	$\frac{d y}{d x} = \frac{3 x}{y}$
71524	Solve the Differential Equation	(dy)/(dx)=6x(y-1)^(2/3)	$\frac{d y}{d x} = 6 x {(y - 1)}^{\frac{2}{3}}$
71525	Solve the Differential Equation	(dy)/(dx)=(3x^2)/(2y)	$\frac{d y}{d x} = \frac{3 x^{2}}{2 y}$
71526	Solve the Differential Equation	(dy)/(dx)=(x+y)^2	$\frac{d y}{d x} = {(x + y)}^{2}$
71527	Solve the Differential Equation	(sin(y)-ysin(x))dx+(cos(x)+xcos(y)-y)dy=0	$(\sin (y) - y \sin (x)) d x + (\cos (x) + x \cos (y) - y) d y = 0$
71528	Solve the Differential Equation	y''''=2xy+3x^2ye^(x^3)	$y'' = 2 x y + 3 x^{2} y e^{x^{3}}$
71529	Solve the Differential Equation	(dy)/(dx)=3e^(-2x)	$\frac{d y}{d x} = 3 e^{- 2 x}$
71530	Solve the Differential Equation	(x^3+xy^2+y)dx+(y^3+x^2y+x)dy=0	$(x^{3} + x y^{2} + y) d x + (y^{3} + x^{2} y + x) d y = 0$
71531	Solve the Differential Equation	5y^4(dy)/(dx)=8x	$5 y^{4} \frac{d y}{d x} = 8 x$
71532	Solve the Differential Equation	(dy)/(dx)=(10x^2)/( square root of 1+x^3)	$\frac{d y}{d x} = \frac{10 x^{2}}{\sqrt{1 + x^{3}}}$
71533	Solve the Differential Equation	(dy)/(dx)=3x	$\frac{d y}{d x} = 3 x$
71534	Solve the Differential Equation	(dy)/(dx)=xy-3x-2y+6	$\frac{d y}{d x} = x y - 3 x - 2 y + 6$
71535	Solve the Differential Equation	(x^2+4)(dy)/(dx)=xy	$(x^{2} + 4) \frac{d y}{d x} = x y$
71536	Solve the Differential Equation	ydx-4(x+y^6)dy=0	$yd x - 4 (x + y^{6}) d y = 0$
71537	Solve the Differential Equation	y''''+2y=x	$y'' + 2 y = x$
71538	Solve the Differential Equation	2x(yd)x+(x^2+1)dy=0	$2 x yd x + (x^{2} + 1) d y = 0$
71539	Solve the Differential Equation	(3x^2+4xy)dx+(2x^2+2y)dy=0	$(3 x^{2} + 4 x y) d x + (2 x^{2} + 2 y) d y = 0$
71540	Solve the Differential Equation	t^2(dy)/(dt)+y^2=ty	$t^{2} \frac{d y}{d t} + y^{2} = t y$
71541	Solve the Differential Equation	x(dy)/(dx)+y=e^x	$x \frac{d y}{d x} + y = e^{x}$
71542	Solve the Differential Equation	(dy)/(dx)-y/x=1	$\frac{d y}{d x} - \frac{y}{x} = 1$
71543	Solve the Differential Equation	(dy)/(dx)=yx^2-1.1y	$\frac{d y}{d x} = y x^{2} - 1.1 y$
71544	Solve the Differential Equation	2xyy''''=1+y^2	$2 x y y'' = 1 + y^{2}$
71545	Solve the Differential Equation	(y-xy^2)dx+(x+x^2y^2)dy=0	$(y - x y^{2}) d x + (x + x^{2} y^{2}) d y = 0$
71546	Solve the Differential Equation	(2xy-3x^2)dx+(x^2+2y)dy=0	$(2 x y - 3 x^{2}) d x + (x^{2} + 2 y) d y = 0$
71547	Solve the Differential Equation	y(2xy+1)dx-xdy=0	$y (2 x y + 1) d x - x d y = 0$
71548	Solve the Differential Equation	(e^(2x)+4)y''''=y	$(e^{2 x} + 4) y'' = y$
71549	Solve the Differential Equation	(dy)/(dx)=2csc(4x)^2	$\frac{d y}{d x} = 2 \csc^{2} (4 x)$
71550	Solve the Differential Equation	y''''=sec(y)^2	$y'' = \sec^{2} (y)$
71551	Solve the Differential Equation	y''''=-y	$y'' = - y$
71552	Solve the Differential Equation	(x^2+2xy-4y^2)dx-(x^2-8xy-4y^2)dy=0	$(x^{2} + 2 x y - 4 y^{2}) d x - (x^{2} - 8 x y - 4 y^{2}) d y = 0$
71553	Solve the Differential Equation	(3x^2y+e^y)dx+(x^3+xe^y-2y)dy=0	$(3 x^{2} y + e^{y}) d x + (x^{3} + x e^{y} - 2 y) d y = 0$
71554	Solve the Differential Equation	(dN)/(dt)+N=Nte^(t+2)	$\frac{d N}{d t} + N = N t e^{t + 2}$
71555	Solve the Differential Equation	y''''=1/3(1+3x)y^4-1/3y	$y'' = \frac{1}{3} (1 + 3 x) y^{4} - \frac{1}{3} y$
71556	Solve the Differential Equation	(dy)/(dt)=y/t	$\frac{d y}{d t} = \frac{y}{t}$
71557	Solve the Differential Equation	(dy)/(dt)=te^(2y)	$\frac{d y}{d t} = t e^{2 y}$
71558	Solve the Differential Equation	xe^(-t)(dx)/(dt)=t	$x e^{- t} \frac{d x}{d t} = t$
71559	Solve the Differential Equation	(dy)/(dx)=(y+3)/(x-4)	$\frac{d y}{d x} = \frac{y + 3}{x - 4}$
71560	Solve the Differential Equation	y(x+y)dx+(x+2y-1)dy=0	$y (x + y) d x + (x + 2 y - 1) d y = 0$
71561	Solve the Differential Equation	(dy)/(dx)+2xy=1	$\frac{d y}{d x} + 2 x y = 1$
71562	Solve the Differential Equation	(dy)/(dx)+2/xy=x^2+2	$\frac{d y}{d x} + \frac{2}{x} y = x^{2} + 2$
71563	Solve the Differential Equation	(z+5)/(4z+19)dz=dy	$\frac{z + 5}{4 z + 19} d z = d y$
71564	Solve the Differential Equation	3y^2(dy)/(dx)=8x	$3 y^{2} \frac{d y}{d x} = 8 x$
71565	Solve the Differential Equation	y^2dx+(x^2+3xy+4y^2)dy=0	$y^{2} d x + (x^{2} + 3 x y + 4 y^{2}) d y = 0$
71566	Solve the Differential Equation	(dy)/(dx)=3x-4	$\frac{d y}{d x} = 3 x - 4$
71567	Solve the Differential Equation	(dy)/(dx)=y/x+e^(y/x)	$\frac{d y}{d x} = \frac{y}{x} + e^{\frac{y}{x}}$
71568	Solve the Differential Equation	(dy)/(dx)=(y^2+xy^2)/(x^2y-x^2)	$\frac{d y}{d x} = \frac{y^{2} + x y^{2}}{x^{2} y - x^{2}}$
71569	Solve the Differential Equation	(2xy-sec(x)^2)dx+(x^2+2y)dy=0	$(2 x y - \sec^{2} (x)) d x + (x^{2} + 2 y) d y = 0$
71570	Solve the Differential Equation	(dy)/(dx)=4xy^2	$\frac{d y}{d x} = 4 x y^{2}$
71571	Solve the Differential Equation	(dy)/(dx)=x^2 square root of y	$\frac{d y}{d x} = x^{2} \sqrt{y}$
71572	Solve the Differential Equation	(dy)/y=(dx)/(1+x)	$\frac{d y}{y} = \frac{d x}{1 + x}$
71573	Solve the Differential Equation	e^y(dy)/(dx)=2x	$e^{y} \frac{d y}{d x} = 2 x$
71574	Solve the Differential Equation	(dy)/(dx)=y/(x natural log of x)	$\frac{d y}{d x} = \frac{y}{x \ln (x)}$
71575	Solve the Differential Equation	y^2dx+2x(yd)y=0	$y^{2} d x + 2 x yd y = 0$
71576	Solve the Differential Equation	(1+y^2)dx+x(yd)y=0	$(1 + y^{2}) d x + x yd y = 0$
71577	Solve the Differential Equation	(1+y)dx-(1-x)dy=0	$(1 + y) d x - (1 - x) d y = 0$
71578	Solve the Differential Equation	x^3+(y+1)^2(dy)/(dx)=0	$x^{3} + {(y + 1)}^{2} \frac{d y}{d x} = 0$
71579	Solve the Differential Equation	xy''''+y=y^2	$x y'' + y = y^{2}$
71580	Solve the Differential Equation	(dy)/(dx)=8/x	$\frac{d y}{d x} = \frac{8}{x}$
71581	Solve the Differential Equation	(dr)/(dtheta)+rsec(theta)=cos(theta)	$\frac{d r}{d θ} + r \sec (θ) = \cos (θ)$
71582	Solve the Differential Equation	3y^2(dy)/(dx)=2x	$3 y^{2} \frac{d y}{d x} = 2 x$
71583	Solve the Differential Equation	(dy)/(dx)+xy=xy^2	$\frac{d y}{d x} + x y = x y^{2}$
71584	Solve the Differential Equation	(dy)/(dx)=(y(2x^2+y^2))/(2x^3)	$\frac{d y}{d x} = \frac{y (2 x^{2} + y^{2})}{2 x^{3}}$
71585	Solve the Differential Equation	y''''+9xe^y=0	$y'' + 9 x e^{y} = 0$
71586	Solve the Differential Equation	xy''''(2y-1)=y(1-x)	$x y'' (2 y - 1) = y (1 - x)$
71587	Solve the Differential Equation	(dy)/(dx)=((1-tan(x))^5)/(cos(x)^2)	$\frac{d y}{d x} = \frac{{(1 - \tan (x))}^{5}}{\cos^{2} (x)}$
71588	Solve the Differential Equation	y''''+5y=0	$y'' + 5 y = 0$
71589	Solve the Differential Equation	7 square root of xy(dy)/(dx)=2	$7 \sqrt{x y} \frac{d y}{d x} = 2$
71590	Solve the Differential Equation	(dy)/(dx)=y(2x-5)	$\frac{d y}{d x} = y (2 x - 5)$
71591	Solve the Differential Equation	(dy)/(dx)=4y^3	$\frac{d y}{d x} = 4 y^{3}$
71592	Solve the Differential Equation	(dy)/(dx) = square root of x	$\frac{d y}{d x} = \sqrt{x}$
71593	Solve the Differential Equation	(2x+3y-1)dx+(2x+3y+2)dy=0	$(2 x + 3 y - 1) d x + (2 x + 3 y + 2) d y = 0$
71594	Solve the Differential Equation	(t+y+1)dt-dy=0	$(t + y + 1) d t - d y = 0$
71595	Solve the Differential Equation	y''''-4y=0	$y'' - 4 y = 0$
71596	Solve the Differential Equation	x(1+3y^2)dy-(1+2x^2)dx=0	$x (1 + 3 y^{2}) d y - (1 + 2 x^{2}) d x = 0$
71597	Solve the Differential Equation	(dy)/(dx)=4x(y^2+1)	$\frac{d y}{d x} = 4 x (y^{2} + 1)$
71598	Solve the Differential Equation	(x+2y-4)dx-(2x+y-5)dy=0	$(x + 2 y - 4) d x - (2 x + y - 5) d y = 0$
71599	Solve the Differential Equation	2x(yd)x+(y^2+x^2)dy=0	$2 x yd x + (y^{2} + x^{2}) d y = 0$
71600	Solve the Differential Equation	(dy)/(dx)+xy=3y+x-3	$\frac{d y}{d x} + x y = 3 y + x - 3$