Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
76201	Solve the Differential Equation	(dy)/(dt)+y=t	$\frac{d y}{d t} + y = t$
76202	Solve the Differential Equation	(y-x^2)dx+xdy=0	$(y - x^{2}) d x + x d y = 0$
76203	Solve the Differential Equation	2(24)(0.5)+2(7)(dy)/(dt)=0	$2 (24) (0.5) + 2 (7) \frac{d y}{d t} = 0$
76204	Solve the Differential Equation	y''''tan(x)=2y-8	$y'' \tan (x) = 2 y - 8$
76205	Solve the Differential Equation	(dy)/(dx)=y/x+7x+9	$\frac{d y}{d x} = \frac{y}{x} + 7 x + 9$
76206	Solve the Differential Equation	yy''''-e^x=0	$y y'' - e^{x} = 0$
76207	Solve the Differential Equation	(x^2-8xy-4y^2)dy=(x^2+2xy-4y^2)dx	$(x^{2} - 8 x y - 4 y^{2}) d y = (x^{2} + 2 x y - 4 y^{2}) d x$
76208	Solve the Differential Equation	(dy)/(dx)+1/2y=3/2	$\frac{d y}{d x} + \frac{1}{2} y = \frac{3}{2}$
76209	Solve the Differential Equation	(x^3+y^3)dx=(xy^2)dy	$(x^{3} + y^{3}) d x = (x y^{2}) d y$
76210	Solve the Differential Equation	(dy)/(dt)=e^t	$\frac{d y}{d t} = e^{t}$
76211	Solve the Differential Equation	xdy=(y+3)dx	$x d y = (y + 3) d x$
76212	Solve the Differential Equation	(2-x)y''''=y	$(2 - x) y'' = y$
76213	Solve the Differential Equation	1/xdy=(e^(x^2))/(y^2)dx	$\frac{1}{x} d y = \frac{e^{x^{2}}}{y^{2}} d x$
76214	Solve the Differential Equation	(dx)/(dt)=x	$\frac{d x}{d t} = x$
76215	Solve the Differential Equation	4y(dy)/(dx)=5x^2	$4 y \frac{d y}{d x} = 5 x^{2}$
76216	Solve the Differential Equation	y''''=(-10x-y^2)/(2xy)	$y'' = \frac{- 10 x - y^{2}}{2 x y}$
76217	Solve the Differential Equation	(dA)/(dt)=-7A	$\frac{d A}{d t} = - 7 A$
76218	Solve the Differential Equation	(dy)/(dx)=(cos(x))/(e^y)	$\frac{d y}{d x} = \frac{\cos (x)}{e^{y}}$
76219	Solve the Differential Equation	(dy)/(dx)=2cos(x)(2-y)	$\frac{d y}{d x} = 2 \cos (x) (2 - y)$
76220	Solve the Differential Equation	y''''=-(x^2+y^2)/(2xy)	$y'' = - \frac{x^{2} + y^{2}}{2 x y}$
76221	Solve the Differential Equation	y(x-1)dy+x(y-1)dx=0	$y (x - 1) d y + x (y - 1) d x = 0$
76222	Solve the Differential Equation	(dy)/(dx)=-6x+6x^2	$\frac{d y}{d x} = - 6 x + 6 x^{2}$
76223	Solve the Differential Equation	(dy)/(dx)=4x^(1/4)	$\frac{d y}{d x} = 4 x^{\frac{1}{4}}$
76224	Solve the Differential Equation	(dy)/(dx)+2yy^2=0	$\frac{d y}{d x} + 2 y \cdot y^{2} = 0$
76225	Solve the Differential Equation	x^3+10y(dy)/(dx)=0	$x^{3} + 10 y \frac{d y}{d x} = 0$
76226	Solve the Differential Equation	2xy''''''''=3y''''	$2 x y'''' = 3 y''$
76227	Solve the Differential Equation	x(dy)/(dx)-y=x^2cos(x)	$x \frac{d y}{d x} - y = x^{2} \cos (x)$
76228	Solve the Differential Equation	(dy)/(dx)=0.8-0.1xy	$\frac{d y}{d x} = 0.8 - 0.1 x y$
76229	Solve the Differential Equation	x^2(dw)/(dx) = square root of w(4x+5)	$x^{2} \frac{d w}{d x} = \sqrt{w} (4 x + 5)$
76230	Solve the Differential Equation	y''''=4x+xy	$y'' = 4 x + x y$
76231	Solve the Differential Equation	2yy''''=xe^x	$2 y y'' = x e^{x}$
76232	Solve the Differential Equation	h(y)=y/(1-e^y)	$h (y) = \frac{y}{1 - e^{y}}$
76233	Solve the Differential Equation	(dy)/(dx)=6x^2 square root of y	$\frac{d y}{d x} = 6 x^{2} \sqrt{y}$
76234	Solve the Differential Equation	e^y((dy)/(dx)+1)=1	$e^{y} (\frac{d y}{d x} + 1) = 1$
76235	Solve the Differential Equation	y''''-6y''''+8=0	$y'' - 6 y'' + 8 = 0$
76236	Solve the Differential Equation	(dy)/(dx)=(x^3+y^3)/(x^2y+xy^2)	$\frac{d y}{d x} = \frac{x^{3} + y^{3}}{x^{2} y + x y^{2}}$
76237	Solve the Differential Equation	(dy)/(dx)+9x^2y=x^2	$\frac{d y}{d x} + 9 x^{2} y = x^{2}$
76238	Solve the Differential Equation	(e^(2x)-y)dx+e^xdy=0	$(e^{2 x} - y) d x + e^{x} d y = 0$
76239	Solve the Differential Equation	tan(ydy)+xcos(ydx)^2=0	$\tan (yd y) + x \cos^{2} (yd x) = 0$
76240	Solve the Differential Equation	(dy)/(dx)+4y=x^2e^(-4x)	$\frac{d y}{d x} + 4 y = x^{2} e^{- 4 x}$
76241	Solve the Differential Equation	xy''''+y=6x^2	$x y'' + y = 6 x^{2}$
76242	Solve the Differential Equation	2(8)(6)+2(6)(dy)/(dt)=0	$2 (8) (6) + 2 (6) \frac{d y}{d t} = 0$
76243	Solve the Differential Equation	(dy)/(dx)+4y^2=0	$\frac{d y}{d x} + 4 y^{2} = 0$
76244	Solve the Differential Equation	(y+1)dx+(4x-1)dy=0	$(y + 1) d x + (4 x - 1) d y = 0$
76245	Solve the Differential Equation	(dy(t))/(dt)=2t^2	$\frac{d y (t)}{d t} = 2 t^{2}$
76246	Solve the Differential Equation	(dy)/(dt)=2t^3 square root of y	$\frac{d y}{d t} = 2 t^{3} \sqrt{y}$
76247	Solve the Differential Equation	(dx)/(dy)+2xy^2=0	$\frac{d x}{d y} + 2 x y^{2} = 0$
76248	Solve the Differential Equation	x^2(yd)y=e^ydx	$x^{2} yd y = e^{y} d x$
76249	Solve the Differential Equation	y''''-3y=1	$y'' - 3 y = 1$
76250	Solve the Differential Equation	(dA)/(dt)=4A	$\frac{d A}{d t} = 4 A$
76251	Solve the Differential Equation	(dy)/(dx)=x^-3	$\frac{d y}{d x} = x^{- 3}$
76252	Solve the Differential Equation	(dF)/(dx)=4e^x+4x^2 , F(0)=-8	$\frac{d F}{d x} = 4 e^{x} + 4 x^{2}$ , $F (0) = - 8$
76253	Solve the Differential Equation	(dy)/(y^2)=xdx	$\frac{d y}{y^{2}} = x d x$
76254	Solve the Differential Equation	e^xdx=ydy	$e^{x} d x = yd y$
76255	Solve the Differential Equation	y''''=1/x	$y'' = \frac{1}{x}$
76256	Solve the Differential Equation	xdy-(yd)x=x^2dy	$x d y - yd x = x^{2} d y$
76257	Solve the Differential Equation	(dr)/(dtheta)=pisin(pitheta) , r(0)=2	$\frac{d r}{d θ} = π \sin (π θ)$ , $r (0) = 2$
76258	Solve the Differential Equation	(dy)/(dx)=x^5 , y(0)=8	$\frac{d y}{d x} = x^{5}$ , $y (0) = 8$
76259	Solve the Differential Equation	(y-x^2)dx+(x+y^2)dy=0	$(y - x^{2}) d x + (x + y^{2}) d y = 0$
76260	Solve the Differential Equation	y''''+3y=2xe^(-3x)	$y'' + 3 y = 2 x e^{- 3 x}$
76261	Solve the Differential Equation	y''''''''+4y=cos(x)	$y'''' + 4 y = \cos (x)$
76262	Solve the Differential Equation	(dy)/(dx)=-y+2	$\frac{d y}{d x} = - y + 2$
76263	Solve the Differential Equation	y''''''''-8y''''+17y=0	$y'''' - 8 y'' + 17 y = 0$
76264	Solve the Differential Equation	y''''=(2x+y-3)^(1/2)	$y'' = {(2 x + y - 3)}^{\frac{1}{2}}$
76265	Solve the Differential Equation	(dy)/(dt)=-ay+b	$\frac{d y}{d t} = - a y + b$
76266	Solve the Differential Equation	t^-6y''''(t)=6	$t^{- 6} y'' (t) = 6$
76267	Solve the Differential Equation	y''''=3x(y+4)^2	$y'' = 3 x {(y + 4)}^{2}$
76268	Solve the Differential Equation	y''''''''-y=sin(x)	$y'''' - y = \sin (x)$
76269	Solve the Differential Equation	(dy)/(dt)=y(t-2)	$\frac{d y}{d t} = y (t - 2)$
76270	Solve the Differential Equation	x(dy)/(dx)+3y=x^4-x	$x \frac{d y}{d x} + 3 y = x^{4} - x$
76271	Solve the Differential Equation	(dy)/(dx)-y=2e^x	$\frac{d y}{d x} - y = 2 e^{x}$
76272	Solve the Differential Equation	(dy)/(dx)=x(y-1)	$\frac{d y}{d x} = x (y - 1)$
76273	Solve the Differential Equation	f(x)=(x+4)^(2/3)	$f (x) = {(x + 4)}^{\frac{2}{3}}$
76274	Solve the Differential Equation	(dy)/(dx)=(7x^2)/( square root of 4+x^3)	$\frac{d y}{d x} = \frac{7 x^{2}}{\sqrt{4 + x^{3}}}$
76275	Solve the Differential Equation	(dp)/(dt)=t^2p-2p+t^2-2	$\frac{d p}{d t} = t^{2} p - 2 p + t^{2} - 2$
76276	Solve the Differential Equation	(dy)/(dx)+(x^2)/y=0	$\frac{d y}{d x} + \frac{x^{2}}{y} = 0$
76277	Solve the Differential Equation	(dy)/(dx)=(sec(x)^2)/(tan(x)^2)	$\frac{d y}{d x} = \frac{\sec^{2} (x)}{\tan^{2} (x)}$
76278	Solve the Differential Equation	(dz)/(dt)=z+zt^2	$\frac{d z}{d t} = z + z t^{2}$
76279	Solve the Differential Equation	((d^2y)/(dx^2))^(3/2)+y=x	${(\frac{d^{2} y}{d x^{2}})}^{\frac{3}{2}} + y = x$
76280	Solve the Differential Equation	(dy)/(dx)=4x+cos(3x)	$\frac{d y}{d x} = 4 x + \cos (3 x)$
76281	Solve the Differential Equation	x^2-y^2+xy(dy)/(dx)=0	$x^{2} - y^{2} + x y \frac{d y}{d x} = 0$
76282	Solve the Differential Equation	(dy)/(dx)=5-8x	$\frac{d y}{d x} = 5 - 8 x$
76283	Solve the Differential Equation	(dy)/(dx)=7-2x	$\frac{d y}{d x} = 7 - 2 x$
76284	Solve the Differential Equation	x(dy)/(dx)-4y=0	$x \frac{d y}{d x} - 4 y = 0$
76285	Solve the Differential Equation	(dy)/(dx)=4e^x	$\frac{d y}{d x} = 4 e^{x}$
76286	Solve the Differential Equation	(x^2+1)dx+x^2y^2dy=0	$(x^{2} + 1) d x + x^{2} y^{2} d y = 0$
76287	Solve the Differential Equation	(dx)/(dt)=x^2-7x	$\frac{d x}{d t} = x^{2} - 7 x$
76288	Solve the Differential Equation	f(x) = natural log of 11x	$f (x) = \ln (11 x)$
76289	Solve the Differential Equation	(dQ)/(dt)+2/(10+2t)Q=4	$\frac{d Q}{d t} + \frac{2}{10 + 2 t} Q = 4$
76290	Solve the Differential Equation	(dy)/(dx)=-x/(3y)	$\frac{d y}{d x} = - \frac{x}{3 y}$
76291	Verify the Differential Equation Solution	(dy)/(dx)=(y^2-1)/(x^2-1) , y(2)=2	$\frac{d y}{d x} = \frac{y^{2} - 1}{x^{2} - 1}$ , $y (2) = 2$
76292	Solve the Differential Equation	(dy)/(dx)=sec(x)^2(2+y)^2 , y(pi)=-5	$\frac{d y}{d x} = \sec^{2} (x) {(2 + y)}^{2}$ , $y (π) = - 5$
76293	Solve the Differential Equation	(dy)/(dx)=e^xy^2+y^2	$\frac{d y}{d x} = e^{x} y^{2} + y^{2}$
76294	Solve the Differential Equation	(y-x+xycot(x))dx+xdy=0	$(y - x + x y \cot (x)) d x + x d y = 0$
76295	Solve the Differential Equation	y''''=x-2ycot(2x)	$y'' = x - 2 y \cot (2 x)$
76296	Solve the Differential Equation	(dt)/(dn)-t=e^(3n)-nt	$\frac{d t}{d n} - t = e^{3 n} - n t$
76297	Solve the Differential Equation	x(dy)/(dx)+(1+11x)y=44	$x \frac{d y}{d x} + (1 + 11 x) y = 44$
76298	Solve the Differential Equation	(x-y)dx+xdy=0	$(x - y) d x + x d y = 0$
76299	Solve the Differential Equation	y''''=y/x+e^(y/x)	$y'' = \frac{y}{x} + e^{\frac{y}{x}}$
76300	Solve the Differential Equation	(dy)/(dx)-(2y)/x=2y^3	$\frac{d y}{d x} - \frac{2 y}{x} = 2 y^{3}$