Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
73801	Solve the Differential Equation	(dy)/(dx)-xy=0	$\frac{d y}{d x} - x y = 0$
73802	Solve the Differential Equation	x^2y''''=1/yx^5	$x^{2} y'' = \frac{1}{y} x^{5}$
73803	Verify the Differential Equation Solution	x^2(dy)/(dx)=y-xy , y(-1)=-1	$x^{2} \frac{d y}{d x} = y - x y$ , $y (- 1) = - 1$
73804	Solve the Differential Equation	y''''=y^2+1	$y'' = y^{2} + 1$
73805	Solve the Differential Equation	y''''+2xy=e^(-x^2)	$y'' + 2 x y = e^{- x^{2}}$
73806	Solve the Differential Equation	y''''=x/y+y/x	$y'' = \frac{x}{y} + \frac{y}{x}$
73807	Solve the Differential Equation	(dz)/(dt)=-e^(t+z)	$\frac{d z}{d t} = - e^{t + z}$
73808	Solve the Differential Equation	y''''=2-y	$y'' = 2 - y$
73809	Solve the Differential Equation	5(dy)/(dtheta)=(e^ysin(theta)^2)/(ysec(theta))	$5 \frac{d y}{d θ} = \frac{e^{y} \sin^{2} (θ)}{y \sec (θ)}$
73810	Solve the Differential Equation	ydx+(1-x)dy=0	$yd x + (1 - x) d y = 0$
73811	Solve the Differential Equation	(dy)/(dx)=x^2(y-1)	$\frac{d y}{d x} = x^{2} (y - 1)$
73812	Solve the Differential Equation	2y''''''''+y=9e^(2t)	$2 y'''' + y = 9 e^{2 t}$
73813	Solve the Differential Equation	(dx)/(dt)=e^(x+t)	$\frac{d x}{d t} = e^{x + t}$
73814	Solve the Differential Equation	xy''''+2y=4x^2	$x y'' + 2 y = 4 x^{2}$
73815	Solve the Differential Equation	(x^2+y)dx+(y+1)^2dy=0	$(x^{2} + y) d x + {(y + 1)}^{2} d y = 0$
73816	Solve the Differential Equation	(1+x)(yd)x+(1-y)xdy=0	$(1 + x) yd x + (1 - y) x d y = 0$
73817	Solve the Differential Equation	y_1''''=y_2^3-2y_2y_1	$y_{1}'' = {y_{2}}^{3} - 2 y_{2} y_{1}$
73818	Solve the Differential Equation	y''''''''+64y=0	$y'''' + 64 y = 0$
73819	Solve the Differential Equation	y''''+3y''''+2y=6	$y'' + 3 y'' + 2 y = 6$
73820	Solve the Differential Equation	(3x^2-2xy+2)dx+(6y^2-x^2+3)dy=0	$(3 x^{2} - 2 x y + 2) d x + (6 y^{2} - x^{2} + 3) d y = 0$
73821	Solve the Differential Equation	(dy)/(dx)+y/x=1/x	$\frac{d y}{d x} + \frac{y}{x} = \frac{1}{x}$
73822	Solve the Differential Equation	(dx)/(dt)=x^2t^2	$\frac{d x}{d t} = x^{2} t^{2}$
73823	Solve the Differential Equation	dy+ydx=e^(-x)dx	$d y + yd x = e^{- x} d x$
73824	Solve the Differential Equation	(dy)/(dx)+y=y^2sin(x)	$\frac{d y}{d x} + y = y^{2} \sin (x)$
73825	Solve the Differential Equation	(dy)/(dx)=yx^4	$\frac{d y}{d x} = y x^{4}$
73826	Solve the Differential Equation	2y''''''''+y=0	$2 y'''' + y = 0$
73827	Solve the Differential Equation	xdy-(yd)x = square root of x^2+y^2dx	$x d y - yd x = \sqrt{x^{2} + y^{2}} d x$
73828	Solve the Differential Equation	(dy)/(dx)=6x-30	$\frac{d y}{d x} = 6 x - 30$
73829	Solve the Differential Equation	y''''=2 square root of y	$y'' = 2 \sqrt{y}$
73830	Solve the Differential Equation	y''''=(y^2+x^2)/(2xy)	$y'' = \frac{y^{2} + x^{2}}{2 x y}$
73831	Solve the Differential Equation	(dy)/(dx)=(3x+xy^2)/(y+x^2y)	$\frac{d y}{d x} = \frac{3 x + x y^{2}}{y + x^{2} y}$
73832	Solve the Differential Equation	e^(-y)(1+(dy)/(dx))=1	$e^{- y} (1 + \frac{d y}{d x}) = 1$
73833	Solve the Differential Equation	(dr)/(ds)=0.4r	$\frac{d r}{d s} = 0.4 r$
73834	Solve the Differential Equation	(dr)/(dtheta)=pisin(pitheta) , r(2)=2	$\frac{d r}{d θ} = π \sin (π θ)$ , $r (2) = 2$
73835	Solve the Differential Equation	(dy)/(dx)=2ycos(2x)	$\frac{d y}{d x} = 2 y \cos (2 x)$
73836	Solve the Differential Equation	y''''=xe^(-sin(x))-ycos(x)	$y'' = x e^{- \sin (x)} - y \cos (x)$
73837	Solve the Differential Equation	(dy)/(dx)+y/x=y^2x	$\frac{d y}{d x} + \frac{y}{x} = y^{2} x$
73838	Solve the Differential Equation	y''''-y''''*2=y^4	$y'' - y'' \cdot 2 = y^{4}$
73839	Solve the Differential Equation	xdx- square root of 1-x^4dy=x^2 square root of 1-x^4dy	$x d x - \sqrt{1 - x^{4}} d y = x^{2} \sqrt{1 - x^{4}} d y$
73840	Solve the Differential Equation	2x(yd)x+x^2dy=0	$2 x yd x + x^{2} d y = 0$
73841	Solve the Differential Equation	(dA)/(dr)=Ab^2cos(br) , A(0)=b^3	$\frac{d A}{d r} = A b^{2} \cos (b r)$ , $A (0) = b^{3}$
73842	Solve the Differential Equation	(y/x+6x)dx+( natural log of x-2)dy=0	$(\frac{y}{x} + 6 x) d x + (\ln (x) - 2) d y = 0$
73843	Solve the Differential Equation	(x^2-2)(dy)/(dx)-xy=0	$(x^{2} - 2) \frac{d y}{d x} - x y = 0$
73844	Solve the Differential Equation	2x(1+y^2)-y(dy)/(dx)(1+x^2)=0	$2 x (1 + y^{2}) - y \frac{d y}{d x} (1 + x^{2}) = 0$
73845	Solve the Differential Equation	(dy)/(dx)=3x^2-4 , y(0)=4	$\frac{d y}{d x} = 3 x^{2} - 4$ , $y (0) = 4$
73846	Solve the Differential Equation	(x^2+1)y''''+3x(y-1)=0	$(x^{2} + 1) y'' + 3 x (y - 1) = 0$
73847	Solve the Differential Equation	(dy)/(dx)=6xy^2	$\frac{d y}{d x} = 6 x y^{2}$
73848	Solve the Differential Equation	(d^2y)/(dx^2)=3x^2+x-2	$\frac{d^{2} y}{d x^{2}} = 3 x^{2} + x - 2$
73849	Solve the Differential Equation	(dy)/(dt)=(t+4)/y	$\frac{d y}{d t} = \frac{t + 4}{y}$
73850	Solve the Differential Equation	y''''''''-2y''''=0	$y'''' - 2 y'' = 0$
73851	Solve the Differential Equation	1/2(di)/(dt)+10i=12	$\frac{1}{2} \cdot \frac{d i}{d t} + 10 i = 12$
73852	Solve the Differential Equation	(dy)/(dx)=(4x^2)/( square root of 5+x^3)	$\frac{d y}{d x} = \frac{4 x^{2}}{\sqrt{5 + x^{3}}}$
73853	Solve the Differential Equation	cos(x)(dy)/(dx)+ysin(x)=cos(x)^2	$\cos (x) \frac{d y}{d x} + y \sin (x) = \cos^{2} (x)$
73854	Solve the Differential Equation	(dy)/(dt)=y(4t^3+1)	$\frac{d y}{d t} = y (4 t^{3} + 1)$
73855	Solve the Differential Equation	(dy)/(dx)=(x^3-21x)/(5+4x-x^2)x^3	$\frac{d y}{d x} = \frac{x^{3} - 21 x}{5 + 4 x - x^{2}} x^{3}$
73856	Solve the Differential Equation	(dy)/(dx)=y^3xe^(x^2)	$\frac{d y}{d x} = y^{3} x e^{x^{2}}$
73857	Solve the Differential Equation	(dy)/(dx)=8x square root of 16-y^2	$\frac{d y}{d x} = 8 x \sqrt{16 - y^{2}}$
73858	Solve the Differential Equation	x square root of 1+y^2dx=y square root of 1+x^2dy	$x \sqrt{1 + y^{2}} d x = y \sqrt{1 + x^{2}} d y$
73859	Solve the Differential Equation	2x(y+1)dx-(x^2+1)dy=0	$2 x (y + 1) d x - (x^{2} + 1) d y = 0$
73860	Solve the Differential Equation	y''''-2ty=t	$y'' - 2 t y = t$
73861	Solve the Differential Equation	(dy)/(dx)=10e^(-5x)	$\frac{d y}{d x} = 10 e^{- 5 x}$
73862	Solve the Differential Equation	(du)/(dt)=(2t+sec(t)^2)/(2u) , u(0)=-2	$\frac{d u}{d t} = \frac{2 t + \sec^{2} (t)}{2 u}$ , $u (0) = - 2$
73863	Solve the Differential Equation	(dy)/(dt)=24t^5	$\frac{d y}{d t} = 24 t^{5}$
73864	Solve the Differential Equation	(4xy^2+3y)dx+(3x^2y+2x)dy=0	$(4 x y^{2} + 3 y) d x + (3 x^{2} y + 2 x) d y = 0$
73865	Solve the Differential Equation	y''''+2y=8	$y'' + 2 y = 8$
73866	Solve the Differential Equation	(dy)/(dx)=26x	$\frac{d y}{d x} = 26 x$
73867	Solve the Differential Equation	yy''''=7cos(x)	$y y'' = 7 \cos (x)$
73868	Solve the Differential Equation	x(dy)/(dx)-y-5x^4-3x^2+2x=0	$x \frac{d y}{d x} - y - 5 x^{4} - 3 x^{2} + 2 x = 0$
73869	Solve the Differential Equation	(dx)/(dy)=(x^2+1)/(2-2y)	$\frac{d x}{d y} = \frac{x^{2} + 1}{2 - 2 y}$
73870	Solve the Differential Equation	y''''-(2y)/x=x^2e^x	$y'' - \frac{2 y}{x} = x^{2} e^{x}$
73871	Solve the Differential Equation	(dy)/(dx)=1-x+y-xy	$\frac{d y}{d x} = 1 - x + y - x y$
73872	Solve the Differential Equation	(dx)/(dt)=x^2	$\frac{d x}{d t} = x^{2}$
73873	Solve the Differential Equation	y''''=x^2-y^2	$y'' = x^{2} - y^{2}$
73874	Solve the Differential Equation	(2x+3y-1)dx+(4x+6y-5)dy=0	$(2 x + 3 y - 1) d x + (4 x + 6 y - 5) d y = 0$
73875	Solve the Differential Equation	y''''+4y''''+13y=0	$y'' + 4 y'' + 13 y = 0$
73876	Solve the Differential Equation	(ds)/(dt)=36t(9t^2-7)^3 , s(1)=1	$\frac{d s}{d t} = 36 t {(9 t^{2} - 7)}^{3}$ , $s (1) = 1$
73877	Solve the Differential Equation	(dy)/(dx)=2y-4	$\frac{d y}{d x} = 2 y - 4$
73878	Solve the Differential Equation	(ds)/(dt)=28t(7t^2-5)^3 , s(1)=15	$\frac{d s}{d t} = 28 t {(7 t^{2} - 5)}^{3}$ , $s (1) = 15$
73879	Solve the Differential Equation	4y(dy)/(dx)=3x^2	$4 y \frac{d y}{d x} = 3 x^{2}$
73880	Solve the Differential Equation	(dy)/(dx)-3y^2cos(3x)=0	$\frac{d y}{d x} - 3 y^{2} \cos (3 x) = 0$
73881	Solve the Differential Equation	(dy)/(dx)=2xy-6x	$\frac{d y}{d x} = 2 x y - 6 x$
73882	Solve the Differential Equation	(dA)/(dt)=-5A	$\frac{d A}{d t} = - 5 A$
73883	Solve the Differential Equation	(dy)/(dx)+x^2y=0	$\frac{d y}{d x} + x^{2} y = 0$
73884	Solve the Differential Equation	(du)/(dt)=3+3u+t+tu	$\frac{d u}{d t} = 3 + 3 u + t + t u$
73885	Solve the Differential Equation	(x+y)dx+(x+y+1)dy=0	$(x + y) d x + (x + y + 1) d y = 0$
73886	Solve the Differential Equation	(dy)/(dx)=(3x^2-4x)/4	$\frac{d y}{d x} = \frac{3 x^{2} - 4 x}{4}$
73887	Solve the Differential Equation	4 square root of xy(dy)/(dx)=1	$4 \sqrt{x y} \frac{d y}{d x} = 1$
73888	Solve the Differential Equation	(dy)/(dt)=(te^t)/(y square root of 5+y^2)	$\frac{d y}{d t} = \frac{t e^{t}}{y \sqrt{5 + y^{2}}}$
73889	Solve the Differential Equation	(dy)/(dx)=(30x)/(e^y)	$\frac{d y}{d x} = \frac{30 x}{e^{y}}$
73890	Solve the Differential Equation	y''''-7y=sin(2x)	$y'' - 7 y = \sin (2 x)$
73891	Solve the Differential Equation	(dy)/(dx)=(x^2)/(y^2+1)	$\frac{d y}{d x} = \frac{x^{2}}{y^{2} + 1}$
73892	Solve the Differential Equation	(4x-2y+5)dx+(2y-2x)dy=0	$(4 x - 2 y + 5) d x + (2 y - 2 x) d y = 0$
73893	Solve the Differential Equation	(d^2R)/(dt^2)=-k/(R^2)	$\frac{d^{2} R}{d t^{2}} = - \frac{k}{R^{2}}$
73894	Solve the Differential Equation	5y(dy)/(dx)=9x^2	$5 y \frac{d y}{d x} = 9 x^{2}$
73895	Solve the Differential Equation	(du)/(dt)=(2t+sec(t)^2)/(2u)	$\frac{d u}{d t} = \frac{(2 t + \sec^{2} (t))}{2 u}$
73896	Solve the Differential Equation	(ds)/(dt)=20t(5t^2-3)^3 , s(1)=5	$\frac{d s}{d t} = 20 t {(5 t^{2} - 3)}^{3}$ , $s (1) = 5$
73897	Solve the Differential Equation	(2x-3y+4)dx+(3x-2y+1)dy=0	$(2 x - 3 y + 4) d x + (3 x - 2 y + 1) d y = 0$
73898	Solve the Differential Equation	x^2y''''+y=0	$x^{2} y'' + y = 0$
73899	Solve the Differential Equation	y''''(x natural log of x)+y=xsin(2x)	$y'' (x \ln (x)) + y = x \sin (2 x)$
73900	Solve the Differential Equation	(dN)/(dt)=2(1-cos((2pit)/24))N	$\frac{d N}{d t} = 2 (1 - \cos (\frac{2 π t}{24})) N$