Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72401	Solve the Differential Equation	(dy)/(dx)=(y-1)/(x^2)	$\frac{d y}{d x} = \frac{y - 1}{x^{2}}$
72402	Solve the Differential Equation	(ds)/(dt)=12t(3t^2-1)^3 , s(1)=3	$\frac{d s}{d t} = 12 t {(3 t^{2} - 1)}^{3}$ , $s (1) = 3$
72403	Solve the Differential Equation	(dy)/(dx)=(x-2)/x	$\frac{d y}{d x} = \frac{x - 2}{x}$
72404	Solve the Differential Equation	e^(-y)sin(x)+(dy)/(dx)=0	$e^{- y} \sin (x) + \frac{d y}{d x} = 0$
72405	Solve the Differential Equation	y/xdx+(y^3- natural log of x)dy=0	$\frac{y}{x} d x + (y^{3} - \ln (x)) d y = 0$
72406	Solve the Differential Equation	(dy)/(dx)=(1+y)e^x	$\frac{d y}{d x} = (1 + y) e^{x}$
72407	Solve the Differential Equation	19(dx)/(dt)+33.6=0	$19 \frac{d x}{d t} + 33.6 = 0$
72408	Solve the Differential Equation	sin(y)(x+sin(y))dx+2x^2cos(ydy)=0	$\sin (y) (x + \sin (y)) d x + 2 x^{2} \cos (yd y) = 0$
72409	Solve the Differential Equation	(dy)/(dt)+y/t=3t , y(2)=8	$\frac{d y}{d t} + \frac{y}{t} = 3 t$ , $y (2) = 8$
72410	Solve the Differential Equation	y''''''''''''-y''''=0	$y'''''' - y'' = 0$
72411	Solve the Differential Equation	y''''=-1.5y	$y'' = - 1.5 y$
72412	Solve the Differential Equation	(2xy-3x^2)dx+(x^2-2y)dy=0	$(2 x y - 3 x^{2}) d x + (x^{2} - 2 y) d y = 0$
72413	Solve the Differential Equation	(dQ)/(dt)+2/(20-t)Q=4	$\frac{d Q}{d t} + \frac{2}{20 - t} Q = 4$
72414	Solve the Differential Equation	(dx)/(dy)=(x^2)/y	$\frac{d x}{d y} = \frac{x^{2}}{y}$
72415	Solve the Differential Equation	(dy)/(dx)=(12x)/y	$\frac{d y}{d x} = \frac{12 x}{y}$
72416	Solve the Differential Equation	xy^3dx+(x^2y^2+1)dy=0	$x y^{3} d x + (x^{2} y^{2} + 1) d y = 0$
72417	Solve the Differential Equation	(x+2)^2(dy)/(dx)=5-8y-4xy	${(x + 2)}^{2} \frac{d y}{d x} = 5 - 8 y - 4 x y$
72418	Solve the Differential Equation	xy''''=y+x	$x y'' = y + x$
72419	Solve the Differential Equation	(dy)/(dx)=2-x+x^3	$\frac{d y}{d x} = 2 - x + x^{3}$
72420	Solve the Differential Equation	(dy)/(dx)=3y^2-y^2sin(x)	$\frac{d y}{d x} = 3 y^{2} - y^{2} \sin (x)$
72421	Solve the Differential Equation	y''''=x^3-2xy	$y'' = x^{3} - 2 x y$
72422	Approximate Using Euler's Method	(dy)/(dx)=e^x , y(0)=0 , t=1 , h=0.1	$\frac{d y}{d x} = e^{x}$ , $y (0) = 0$ , $t = 1$ , $h = 0.1$
72423	Solve the Differential Equation	(d^2y)/(dx^2)=-3/(x^4)	$\frac{d^{2} y}{d x^{2}} = - \frac{3}{x^{4}}$
72424	Solve the Differential Equation	e^(4x)dx-sin(4(yd)y)=0	$e^{4 x} d x - \sin (4 yd y) = 0$
72425	Solve the Differential Equation	(dy)/(dx)=7e^(x-y)	$\frac{d y}{d x} = 7 e^{x - y}$
72426	Solve the Differential Equation	(3x+2y)dx+2xdy=0	$(3 x + 2 y) d x + 2 x d y = 0$
72427	Solve the Differential Equation	f(x) = square root of x	$f (x) = \sqrt{x}$
72428	Solve the Differential Equation	(dy)/(dx)=(cos(x))/(sin(y))	$\frac{d y}{d x} = \frac{\cos (x)}{\sin (y)}$
72429	Solve the Differential Equation	y^2dx+x(x+y)dy=0	$y^{2} d x + x (x + y) d y = 0$
72430	Solve the Differential Equation	(dx)/(dy)+(4/(y+1))x=y/(y+1)	$\frac{d x}{d y} + (\frac{4}{y + 1}) x = \frac{y}{y + 1}$
72431	Solve the Differential Equation	(x+y)dx+(x+y-5)dy=0	$(x + y) d x + (x + y - 5) d y = 0$
72432	Solve the Differential Equation	xdx+y^-1dy=0	$x d x + y^{- 1} d y = 0$
72433	Solve the Differential Equation	(dy)/(dx)=-7y	$\frac{d y}{d x} = - 7 y$
72434	Solve the Differential Equation	x(dy)/(dx)=2-4x^3	$x \frac{d y}{d x} = 2 - 4 x^{3}$
72435	Solve the Differential Equation	x(yd)y-(x^2+2)dx=0	$x yd y - (x^{2} + 2) d x = 0$
72436	Solve the Differential Equation	(dy)/(dx)=-xy^2	$\frac{d y}{d x} = - x y^{2}$
72437	Solve the Differential Equation	(dy)/(dx)=(e^x)/(y^2)	$\frac{d y}{d x} = \frac{e^{x}}{y^{2}}$
72438	Solve the Differential Equation	(dy)/(dx)+6y=12	$\frac{d y}{d x} + 6 y = 12$
72439	Solve the Differential Equation	y''''=(2x^2-3x)(x-5)	$y'' = (2 x^{2} - 3 x) (x - 5)$
72440	Solve the Differential Equation	y''''=x/(2x^2-7)	$y'' = \frac{x}{2 x^{2} - 7}$
72441	Solve the Differential Equation	(dy)/(dx)=y^2(1-8x)	$\frac{d y}{d x} = y^{2} (1 - 8 x)$
72442	Solve the Differential Equation	y''''=ay+b	$y'' = a y + b$
72443	Solve the Differential Equation	(dy)/(dx)+8x^3=3x^2	$\frac{d y}{d x} + 8 x^{3} = 3 x^{2}$
72444	Solve the Differential Equation	(dy)/(dx)=1/(x+y+1)	$\frac{d y}{d x} = \frac{1}{x + y + 1}$
72445	Solve the Differential Equation	(dy)/(dx)=-6x+9x^2	$\frac{d y}{d x} = - 6 x + 9 x^{2}$
72446	Solve the Differential Equation	(x+2y)dx+(2x+3y)dy=0	$(x + 2 y) d x + (2 x + 3 y) d y = 0$
72447	Solve the Differential Equation	(dy)/(dx)=(x-3)e^(-2y)	$\frac{d y}{d x} = (x - 3) e^{- 2 y}$
72448	Solve the Differential Equation	(dy)/(dx)-x square root of y=0	$\frac{d y}{d x} - x \sqrt{y} = 0$
72449	Solve the Differential Equation	(dy)/(dx)=(e^(2x))/(4y^3)	$\frac{d y}{d x} = \frac{e^{2 x}}{4 y^{3}}$
72450	Solve the Differential Equation	ydx+(2x-y)dy=0	$yd x + (2 x - y) d y = 0$
72451	Solve the Differential Equation	y(x^2+xy-2y^2)dx+x(3y^2-xy-x^2)dy=0	$y (x^{2} + x y - 2 y^{2}) d x + x (3 y^{2} - x y - x^{2}) d y = 0$
72452	Solve the Differential Equation	y''''=(9x)/y	$y'' = \frac{9 x}{y}$
72453	Solve the Differential Equation	y''''''''''''-4y''''''''-5y''''=0	$y'''''' - 4 y'''' - 5 y'' = 0$
72454	Solve the Differential Equation	(d^2y)/(dx^2)=-y	$\frac{d^{2} y}{d x^{2}} = - y$
72455	Solve the Differential Equation	y''''''''+y=2xsin(x)	$y'''' + y = 2 x \sin (x)$
72456	Solve the Differential Equation	(dy)/(dx)=(2y)/x+sin(y/(x^2))	$\frac{d y}{d x} = \frac{2 y}{x} + \sin (\frac{y}{x^{2}})$
72457	Solve the Differential Equation	(4+x^2)dy+4dx=0	$(4 + x^{2}) d y + 4 d x = 0$
72458	Solve the Differential Equation	(dy)/(dx)=12xy	$\frac{d y}{d x} = 12 x y$
72459	Solve the Differential Equation	y^(1/2)(dy)/(dx)+y^(3/2)=1	$y^{\frac{1}{2}} \frac{d y}{d x} + y^{\frac{3}{2}} = 1$
72460	Solve the Differential Equation	(dy)/(dx)+4y=x-2x^2	$\frac{d y}{d x} + 4 y = x - 2 x^{2}$
72461	Solve the Differential Equation	(dy)/(dx)=(2x^2+2y^2)/(xy)	$\frac{d y}{d x} = \frac{2 x^{2} + 2 y^{2}}{x y}$
72462	Solve the Differential Equation	(dy)/( square root of x)=(3dx)/( square root of y)	$\frac{d y}{\sqrt{x}} = \frac{3 d x}{\sqrt{y}}$
72463	Solve the Differential Equation	y(2xy+1)dx+x(1+2xy-x^3y^3)dy=0	$y (2 x y + 1) d x + x (1 + 2 x y - x^{3} y^{3}) d y = 0$
72464	Solve the Differential Equation	(4y-3x)dx+5xdy=0	$(4 y - 3 x) d x + 5 x d y = 0$
72465	Solve the Differential Equation	(cos(x)cos(y)-cot(x))dx-sin(x)sin(ydy)=0	$(\cos (x) \cos (y) - \cot (x)) d x - \sin (x) \sin (yd y) = 0$
72466	Solve the Differential Equation	y''''-6y''''=0	$y'' - 6 y'' = 0$
72467	Solve the Differential Equation	(dy)/(dx)=x^2-y^2	$\frac{d y}{d x} = x^{2} - y^{2}$
72468	Solve the Differential Equation	(y-xy^3)dx+xdy=0	$(y - x y^{3}) d x + x d y = 0$
72469	Solve the Differential Equation	DE(dy)/(dx)+Py=0	$D E \frac{d y}{d x} + P y = 0$
72470	Solve the Differential Equation	(dy)/(dx)=4 square root of y^2+7x^2	$\frac{d y}{d x} = 4 \sqrt{y^{2} + 7 x^{2}}$
72471	Solve the Differential Equation	(xy+y^2)dx-x^2dy=0	$(x y + y^{2}) d x - x^{2} d y = 0$
72472	Solve the Differential Equation	(x-4y-3)dx-(x-6y-5)dy=0	$(x - 4 y - 3) d x - (x - 6 y - 5) d y = 0$
72473	Solve the Differential Equation	(r^3+s^3)dr+s^2(3r+ks)ds=0	$(r^{3} + s^{3}) d r + s^{2} (3 r + k s) d s = 0$
72474	Solve the Differential Equation	(dy)/(dx)=-0.7y	$\frac{d y}{d x} = - 0.7 y$
72475	Solve the Differential Equation	(dy)/(dx)=(7-3x)e^(-y)	$\frac{d y}{d x} = (7 - 3 x) e^{- y}$
72476	Solve the Differential Equation	(dy)/(dx)=(40x)/(e^y)	$\frac{d y}{d x} = \frac{40 x}{e^{y}}$
72477	Solve the Differential Equation	(dy)/(dx)=7x^-8	$\frac{d y}{d x} = 7 x^{- 8}$
72478	Solve the Differential Equation	y''''=xy+y	$y'' = x y + y$
72479	Solve the Differential Equation	y''''=2/3x square root of 1-9y^2	$y'' = \frac{2}{3} x \sqrt{1 - 9 y^{2}}$
72480	Solve the Differential Equation	(x^2+1)(dy)/(dx)+3x(y-1)=0	$(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0$
72481	Solve the Differential Equation	(dy)/(dt)=(4t+y+3)^2	$\frac{d y}{d t} = {(4 t + y + 3)}^{2}$
72482	Solve the Differential Equation	(dy)/(dx)=y-4	$\frac{d y}{d x} = y - 4$
72483	Solve the Differential Equation	(dy)/(dx)=ye^x	$\frac{d y}{d x} = y e^{x}$
72484	Solve the Differential Equation	(dy)/(dx)=-0.3y	$\frac{d y}{d x} = - 0.3 y$
72485	Solve the Differential Equation	(x+4)y''''=x+5	$(x + 4) y'' = x + 5$
72486	Solve the Differential Equation	y''''=x/(2y)	$y'' = \frac{x}{2 y}$
72487	Solve the Differential Equation	(4y+2x-5)dx+(6y+4x-1)dy=0	$(4 y + 2 x - 5) d x + (6 y + 4 x - 1) d y = 0$
72488	Solve the Differential Equation	x^2(dy)/(dx)=4x^2+7xy+2y^2	$x^{2} \frac{d y}{d x} = 4 x^{2} + 7 x y + 2 y^{2}$
72489	Solve the Differential Equation	(dy)/(dx)=8x^3-9x^2+3x	$\frac{d y}{d x} = 8 x^{3} - 9 x^{2} + 3 x$
72490	Solve the Differential Equation	xy''''-y=x^2	$x y'' - y = x^{2}$
72491	Solve the Differential Equation	(dy)/(dx)+x^2(3y-2)=0	$\frac{d y}{d x} + x^{2} (3 y - 2) = 0$
72492	Solve the Differential Equation	(x-1)dy+(y-2)dx=0	$(x - 1) d y + (y - 2) d x = 0$
72493	Solve the Differential Equation	natural log of (dy)/(dx)=ax+by	$\ln (\frac{d y}{d x}) = a x + b y$
72494	Solve the Differential Equation	y^3dx+3xy^2dy=0	$y^{3} d x + 3 x y^{2} d y = 0$
72495	Solve the Differential Equation	(dy)/(dx)=0/(1+1)	$\frac{d y}{d x} = \frac{0}{1 + 1}$
72496	Solve the Differential Equation	(dx)/(dt)=5x-3	$\frac{d x}{d t} = 5 x - 3$
72497	Solve the Differential Equation	(dy)/(dx)=8x^3-9x^2+x	$\frac{d y}{d x} = 8 x^{3} - 9 x^{2} + x$
72498	Solve the Differential Equation	(dr)/(dt)=(sec(t)^2)/(tan(t)+1)	$\frac{d r}{d t} = \frac{\sec^{2} (t)}{\tan (t) + 1}$
72499	Solve the Differential Equation	(x^2+4)dy=2x(yd)x	$(x^{2} + 4) d y = 2 x yd x$
72500	Solve the Differential Equation	(dy)/(dt)=-2y	$\frac{d y}{d t} = - 2 y$