Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72801	Solve the Differential Equation	4xy^2dx+(x^2+1)dy=0	$4 x y^{2} d x + (x^{2} + 1) d y = 0$
72802	Solve the Differential Equation	(dy)/(dx)=(7y^2)/x	$\frac{d y}{d x} = \frac{7 y^{2}}{x}$
72803	Solve the Differential Equation	xy''''-2y=2x square root of y	$x y'' - 2 y = 2 x \sqrt[2]{y}$
72804	Solve the Differential Equation	(dy)/(dx)=(y^2+1)/(x^2)	$\frac{d y}{d x} = \frac{y^{2} + 1}{x^{2}}$
72805	Solve the Differential Equation	(ds)/(dt)=28t(7t^2-5)^3 , s(1)=4	$\frac{d s}{d t} = 28 t {(7 t^{2} - 5)}^{3}$ , $s (1) = 4$
72806	Solve the Differential Equation	xdy+(xy+y-1)dx=0	$x d y + (x y + y - 1) d x = 0$
72807	Solve the Differential Equation	e^(-y)sin(x)-(dy)/(dx)cos(x)^2=0	$e^{- y} \sin (x) - \frac{d y}{d x} \cos^{2} (x) = 0$
72808	Solve the Differential Equation	(-20xy^2+6x)dx+(3y^2-20x^2y)dy=0	$(- 20 x y^{2} + 6 x) d x + (3 y^{2} - 20 x^{2} y) d y = 0$
72809	Solve the Differential Equation	(dy)/(dx)-y=2e^xy^2	$\frac{d y}{d x} - y = 2 e^{x} y^{2}$
72810	Solve the Differential Equation	xy''''-y=x	$x y'' - y = x$
72811	Solve the Differential Equation	xy''''=1	$x y'' = 1$
72812	Solve the Differential Equation	x(yd)x+2(x^2+2y^2)dy=0	$x yd x + 2 (x^{2} + 2 y^{2}) d y = 0$
72813	Solve the Differential Equation	(dy)/(dx)=y^2xe^(3x+4y)	$\frac{d y}{d x} = y^{2} x e^{3 x + 4 y}$
72814	Solve the Differential Equation	(du)/(dt)=(2t+sec(t)^2)/(2u) , u(0)=-3	$\frac{d u}{d t} = \frac{2 t + \sec^{2} (t)}{2 u}$ , $u (0) = - 3$
72815	Solve the Differential Equation	y''''''''-4y''''-5y=3t^3	$y'''' - 4 y'' - 5 y = 3 t^{3}$
72816	Solve the Differential Equation	(dy)/(dt)=-4y	$\frac{d y}{d t} = - 4 y$
72817	Solve the Differential Equation	(2+y/x)dx+(x/y+2)dy=0	$(2 + \frac{y}{x}) d x + (\frac{x}{y} + 2) d y = 0$
72818	Solve the Differential Equation	(dy)/(dx)=x/y , y(0)=-9	$\frac{d y}{d x} = \frac{x}{y}$ , $y (0) = - 9$
72819	Solve the Differential Equation	(dW)/(dh)=0.0015h^2	$\frac{d W}{d h} = 0.0015 h^{2}$
72820	Solve the Differential Equation	(dy)/(dx)+ycos(x)=2cos(x)	$\frac{d y}{d x} + y \cos (x) = 2 \cos (x)$
72821	Solve the Differential Equation	7 square root of xy(dy)/(dx)=3	$7 \sqrt{x y} \frac{d y}{d x} = 3$
72822	Solve the Differential Equation	y''''-3y=6x+4	$y'' - 3 y = 6 x + 4$
72823	Solve the Differential Equation	(x+y)(x-y)dx+x(x-2y)dy=0	$(x + y) (x - y) d x + x (x - 2 y) d y = 0$
72824	Solve the Differential Equation	(du)/(dt)=(2t+sec(t)^2)/(2u) , u(0)=-7	$\frac{d u}{d t} = \frac{2 t + \sec^{2} (t)}{2 u}$ , $u (0) = - 7$
72825	Solve the Differential Equation	(dy)/(dx)=1/(y-x)	$\frac{d y}{d x} = \frac{1}{y - x}$
72826	Solve the Differential Equation	(dy)/(dx)=-10x+9x^2	$\frac{d y}{d x} = - 10 x + 9 x^{2}$
72827	Solve the Differential Equation	(ds)/(dt)=20t(5t^2-3)^3 , s(1)=2	$\frac{d s}{d t} = 20 t {(5 t^{2} - 3)}^{3}$ , $s (1) = 2$
72828	Solve the Differential Equation	(dy)/(dx)=y-x^2	$\frac{d y}{d x} = y - x^{2}$
72829	Solve the Differential Equation	(dy)/(dx)=x/(y^2+1)	$\frac{d y}{d x} = \frac{x}{y^{2} + 1}$
72830	Solve the Differential Equation	(dy)/(dx)=4x^3-6x^2+9x	$\frac{d y}{d x} = 4 x^{3} - 6 x^{2} + 9 x$
72831	Solve the Differential Equation	(dy)/(dx)=x-x^2	$\frac{d y}{d x} = x - x^{2}$
72832	Solve the Differential Equation	(dy)/(dx)+1/3y=1/3(1-2x)y^4	$\frac{d y}{d x} + \frac{1}{3} y = \frac{1}{3} (1 - 2 x) y^{4}$
72833	Solve the Differential Equation	xy''''+y=5	$x y'' + y = 5$
72834	Solve the Differential Equation	y''''=4x-y	$y'' = 4 x - y$
72835	Solve the Differential Equation	(dy)/(dx)=-8x+3x^2	$\frac{d y}{d x} = - 8 x + 3 x^{2}$
72836	Solve the Differential Equation	f(x)=2^40	$f (x) = 2^{40}$
72837	Solve the Differential Equation	e^(-y)(1+y'''')=1	$e^{- y} (1 + y'') = 1$
72838	Solve the Differential Equation	(dy)/(dx)=cx+c^2+1	$\frac{d y}{d x} = c x + c^{2} + 1$
72839	Solve the Differential Equation	x^2y(dy)/(dx)=e^y	$x^{2} y \frac{d y}{d x} = e^{y}$
72840	Solve the Differential Equation	y''''+y=2e^x	$y'' + y = 2 e^{x}$
72841	Solve the Differential Equation	(dr)/(dtheta)=picos(pitheta) , r(2)=2	$\frac{d r}{d θ} = π \cos (π θ)$ , $r (2) = 2$
72842	Solve the Differential Equation	(dy)/(dx)=40x	$\frac{d y}{d x} = 40 x$
72843	Solve the Differential Equation	(dy)/(dx)=(y+1)/(x-3)	$\frac{d y}{d x} = \frac{y + 1}{x - 3}$
72844	Solve the Differential Equation	(x^2+xy+3y^2)dx-(x^2+2xy)dy=0	$(x^{2} + x y + 3 y^{2}) d x - (x^{2} + 2 x y) d y = 0$
72845	Solve the Differential Equation	ydx-4(x+y^6)dy=0	$yd x - 4 (x + y^{6}) d y = 0$
72846	Solve the Differential Equation	(x^3+y/x)dx+(y^2+ natural log of x)dy=0	$(x^{3} + \frac{y}{x}) d x + (y^{2} + \ln (x)) d y = 0$
72847	Solve the Differential Equation	2(dy)/(dx)=(4d^7y)/(dx^2)-3	$2 \frac{d y}{d x} = \frac{4 d^{7} y}{d x^{2}} - 3$
72848	Solve the Differential Equation	(ds)/(dt)=20t(5t^2-3)^3 , s(1)=13	$\frac{d s}{d t} = 20 t {(5 t^{2} - 3)}^{3}$ , $s (1) = 13$
72849	Solve the Differential Equation	(dy)/(dx)=-4x^3y	$\frac{d y}{d x} = - 4 x^{3} y$
72850	Solve the Differential Equation	(dy)/(dx)=(3x^2-4x)/25	$\frac{d y}{d x} = \frac{3 x^{2} - 4 x}{25}$
72851	Solve the Differential Equation	x(dy)/(dx)+2y=sin(x)	$x \frac{d y}{d x} + 2 y = \sin (x)$
72852	Solve the Differential Equation	(dy)/(dx)-6xy-12x=0	$\frac{d y}{d x} - 6 x y - 12 x = 0$
72853	Solve the Differential Equation	(dy)/(dx)=y-8	$\frac{d y}{d x} = y - 8$
72854	Solve the Differential Equation	x^2y''''=1-x^2+y^2-x^2y^2	$x^{2} y'' = 1 - x^{2} + y^{2} - x^{2} y^{2}$
72855	Solve the Differential Equation	(dy)/(dx)=x^2e^(-y)	$\frac{d y}{d x} = x^{2} e^{- y}$
72856	Solve the Differential Equation	e^(-y)sec(x)-(dy)/(dx)cos(x)=0	$e^{- y} \sec (x) - \frac{d y}{d x} \cos (x) = 0$
72857	Solve the Differential Equation	y''''+4y''''-2y=2x^2-3x+6	$y'' + 4 y'' - 2 y = 2 x^{2} - 3 x + 6$
72858	Solve the Differential Equation	(dz)/(dt)=-6e^(t+z)	$\frac{d z}{d t} = - 6 e^{t + z}$
72859	Solve the Differential Equation	y''''=(7x)/y	$y'' = \frac{7 x}{y}$
72860	Solve the Differential Equation	(dy)/(dx)=x^2(1-y)	$\frac{d y}{d x} = x^{2} (1 - y)$
72861	Solve the Differential Equation	(dy)/(dx)=(y-3)/(5x)	$\frac{d y}{d x} = \frac{y - 3}{5 x}$
72862	Solve the Differential Equation	(2x+3)+(2y-2)y''''=0	$(2 x + 3) + (2 y - 2) y'' = 0$
72863	Solve the Differential Equation	y''''-7y=e^x	$y'' - 7 y = e^{x}$
72864	Solve the Differential Equation	(dx)/(dy)=x+y	$\frac{d x}{d y} = x + y$
72865	Solve the Differential Equation	(dy)/(dx)=6x square root of 9-y^2	$\frac{d y}{d x} = 6 x \sqrt{9 - y^{2}}$
72866	Solve the Differential Equation	xy^2dx+x^2(yd)y=0	$x y^{2} d x + x^{2} yd y = 0$
72867	Solve the Differential Equation	4x(dy)/(dx)-y=3x^2	$4 x \frac{d y}{d x} - y = 3 x^{2}$
72868	Solve the Differential Equation	x(dy)/(dx)+y=4x , y(1)=8	$x \frac{d y}{d x} + y = 4 x$ , $y (1) = 8$
72869	Solve the Differential Equation	(dy)/(dx)-y=-y^2	$\frac{d y}{d x} - y = - y^{2}$
72870	Solve the Differential Equation	y''''''''=x	$y'''' = x$
72871	Solve the Differential Equation	(dy)/(dx)=e^(3x)+3x	$\frac{d y}{d x} = e^{3 x} + 3 x$
72872	Solve the Differential Equation	y''''+4/xy=x^3y^2	$y'' + \frac{4}{x} y = x^{3} y^{2}$
72873	Solve the Differential Equation	(dy)/(dt)=8y	$\frac{d y}{d t} = 8 y$
72874	Solve the Differential Equation	-(2y)/(t^3)dt+1/(t^2)dy=0	$- \frac{2 y}{t^{3}} d t + \frac{1}{t^{2}} d y = 0$
72875	Solve the Differential Equation	y(x+1)+y''''=0	$y (x + 1) + y'' = 0$
72876	Solve the Differential Equation	xdy+ydx=0	$x d y + yd x = 0$
72877	Solve the Differential Equation	(dy)/(dx)+y^2sin(x)=0	$\frac{d y}{d x} + y^{2} \sin (x) = 0$
72878	Solve the Differential Equation	(dy)/(dtheta)=(e^ysin(theta)^2)/(ysec(theta))	$\frac{d y}{d θ} = \frac{e^{y} \sin^{2} (θ)}{y \sec (θ)}$
72879	Solve the Differential Equation	(dy)/(dx)+y/x=y^3	$\frac{d y}{d x} + \frac{y}{x} = y^{3}$
72880	Solve the Differential Equation	(dy)/(dx)=15x^2	$\frac{d y}{d x} = 15 x^{2}$
72881	Solve the Differential Equation	(x^3+xy^2+y)dy+(x^2y+y^3+x)dx=0	$(x^{3} + x y^{2} + y) d y + (x^{2} y + y^{3} + x) d x = 0$
72882	Solve the Differential Equation	(dy)/(dx)=xy+x	$\frac{d y}{d x} = x y + x$
72883	Solve the Differential Equation	(2xy+3y^2)dx-(2xy+x^2)dy=0	$(2 x y + 3 y^{2}) d x - (2 x y + x^{2}) d y = 0$
72884	Solve the Differential Equation	(dA)/(dt)=8A	$\frac{d A}{d t} = 8 A$
72885	Solve the Differential Equation	square root of 4+y^2dx-(yd)y=x^2(yd)y	$\sqrt{4 + y^{2}} d x - yd y = x^{2} yd y$
72886	Solve the Differential Equation	7y(dy)/(dx)=6x^2	$7 y \frac{d y}{d x} = 6 x^{2}$
72887	Solve the Differential Equation	x^2(dy)/(dx)=3y	$x^{2} \frac{d y}{d x} = 3 y$
72888	Solve the Differential Equation	y''''=(3x)/y	$y'' = \frac{3 x}{y}$
72889	Solve the Differential Equation	(dy)/(dx)-(2y)/x=3x^2	$\frac{d y}{d x} - \frac{2 y}{x} = 3 x^{2}$
72890	Solve the Differential Equation	x^2y^3dx+x^3y^2dy=0	$x^{2} y^{3} d x + x^{3} y^{2} d y = 0$
72891	Solve the Differential Equation	(cos(x)sin(x)-xy^2)dx+y(1-x^2)dy=0	$(\cos (x) \sin (x) - x y^{2}) d x + y (1 - x^{2}) d y = 0$
72892	Solve the Differential Equation	y''''+25y=0	$y'' + 25 y = 0$
72893	Solve the Differential Equation	(dy)/(dx)=-6x+15x^2	$\frac{d y}{d x} = - 6 x + 15 x^{2}$
72894	Solve the Differential Equation	(dy)/(dx)=f(x)	$\frac{d y}{d x} = f (x)$
72895	Solve the Differential Equation	(x+4y^2)dy+2(yd)x=0	$(x + 4 y^{2}) d y + 2 yd x = 0$
72896	Solve the Differential Equation	(sin(2theta)-2pcos(theta))dtheta=2dp	$(\sin (2 θ) - 2 p \cos (θ)) d θ = 2 d p$
72897	Solve the Differential Equation	(dy)/(dx)=(ycos(x))/(1-2y)	$\frac{d y}{d x} = \frac{y \cos (x)}{1 - 2 y}$
72898	Solve the Differential Equation	y''''=5x	$y'' = 5 x$
72899	Solve the Differential Equation	(dy)/(dx)=e^(3x) , y(0)=4	$\frac{d y}{d x} = e^{3 x}$ , $y (0) = 4$
72900	Solve the Differential Equation	(dy)/(dx)=15 square root of xy	$\frac{d y}{d x} = 15 \sqrt{x y}$