Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
71001	Solve the Differential Equation	y''''+y=sec(x)	$y'' + y = \sec (x)$
71002	Solve the Differential Equation	y''''=e^(x+y)	$y'' = e^{x + y}$
71003	Solve the Differential Equation	y''''=xy	$y'' = x y$
71004	Solve the Differential Equation	(dy)/(dt)=63t^8	$\frac{d y}{d t} = 63 t^{8}$
71005	Solve the Differential Equation	(dy)/(dx)=x^(3/2)	$\frac{d y}{d x} = x^{\frac{3}{2}}$
71006	Solve the Differential Equation	y''''=(x^2)/y	$y'' = \frac{x^{2}}{y}$
71007	Solve the Differential Equation	(d^2y)/(dx^2)=(21sec(x)^2tan(x))/10	$\frac{d^{2} y}{d x^{2}} = \frac{21 \sec^{2} (x) \tan (x)}{10}$
71008	Solve the Differential Equation	y''''=x-2y	$y'' = x - 2 y$
71009	Solve the Differential Equation	1/3(dy)/(dx)=y+1/3x^2e^(3x)	$\frac{1}{3} \cdot \frac{d y}{d x} = y + \frac{1}{3} x^{2} e^{3 x}$
71010	Solve the Differential Equation	xy''''+y=2x	$x y'' + y = 2 x$
71011	Solve the Differential Equation	(dy)/(dx)=e^x	$\frac{d y}{d x} = e^{x}$
71012	Solve the Differential Equation	(dy)/(dx)=3e^(x-y)	$\frac{d y}{d x} = 3 e^{x - y}$
71013	Solve the Differential Equation	(x-y^3+y^2sin(x))dx=(3xy^2+2ycos(x))dy	$(x - y^{3} + y^{2} \sin (x)) d x = (3 x y^{2} + 2 y \cos (x)) d y$
71014	Solve the Differential Equation	xy''''+6y=3xy^(4/3)	$x y'' + 6 y = 3 x y^{\frac{4}{3}}$
71015	Solve the Differential Equation	2(y-4x^2)dx+xdy=0	$2 (y - 4 x^{2}) d x + x d y = 0$
71016	Solve the Differential Equation	(2x^2y+2x)(dy)/(dx)+2xy^2+2y=0	$(2 x^{2} y + 2 x) \frac{d y}{d x} + 2 x y^{2} + 2 y = 0$
71017	Solve the Differential Equation	(dy)/(dx)=4x^3-3x^2+x	$\frac{d y}{d x} = 4 x^{3} - 3 x^{2} + x$
71018	Solve the Differential Equation	(dy)/(dt)=15t^4	$\frac{d y}{d t} = 15 t^{4}$
71019	Solve the Differential Equation	y''''=(2y)/x	$y'' = \frac{2 y}{x}$
71020	Solve the Differential Equation	(dy)/(dx)=2x-5	$\frac{d y}{d x} = 2 x - 5$
71021	Solve the Differential Equation	(dy)/(dx)=(3y)/x	$\frac{d y}{d x} = \frac{3 y}{x}$
71022	Solve the Differential Equation	(dy)/(dx)=2x-7	$\frac{d y}{d x} = 2 x - 7$
71023	Solve the Differential Equation	(dy)/(dx)=2x-6	$\frac{d y}{d x} = 2 x - 6$
71024	Solve the Differential Equation	(dy)/(dx)=3x-5	$\frac{d y}{d x} = 3 x - 5$
71025	Solve the Differential Equation	(dy)/(dx)=x-2xy	$\frac{d y}{d x} = x - 2 x y$
71026	Solve the Differential Equation	(dy)/(dx)=6y	$\frac{d y}{d x} = 6 y$
71027	Solve the Differential Equation	(dy)/(dx)=2e^(x-y)	$\frac{d y}{d x} = 2 e^{x - y}$
71028	Solve the Differential Equation	(dy)/(dx)=y^2+1	$\frac{d y}{d x} = y^{2} + 1$
71029	Solve the Differential Equation	y''''''''+y=tan(x)	$y'''' + y = \tan (x)$
71030	Solve the Differential Equation	(x^2-xy+y^2)dx-x(yd)y=0	$(x^{2} - x y + y^{2}) d x - x yd y = 0$
71031	Solve the Differential Equation	(dy)/(dx)=x square root of 1-y^2	$\frac{d y}{d x} = x \sqrt{1 - y^{2}}$
71032	Solve the Differential Equation	(dy)/(dx)=x^2y^2	$\frac{d y}{d x} = x^{2} y^{2}$
71033	Solve the Differential Equation	y''''+4y=0	$y'' + 4 y = 0$
71034	Solve the Differential Equation	3(dy)/(dx)+12y=4	$3 \frac{d y}{d x} + 12 y = 4$
71035	Solve the Differential Equation	(dy)/(dx)=(-x)/y	$\frac{d y}{d x} = \frac{- x}{y}$
71036	Solve the Differential Equation	xy''''+y=x^4-3x	$x y'' + y = x^{4} - 3 x$
71037	Solve the Differential Equation	(dy)/(dt)+csc(y)=0	$\frac{d y}{d t} + \csc (y) = 0$
71038	Solve the Differential Equation	y''''-y=0	$y'' - y = 0$
71039	Solve the Differential Equation	(x+sin(y))dx+(xcos(y)-2y)dy=0	$(x + \sin (y)) d x + (x \cos (y) - 2 y) d y = 0$
71040	Solve the Differential Equation	(2x^3-xy^2-2y+3)dx+(x^2y+2x)dy=0	$(2 x^{3} - x y^{2} - 2 y + 3) d x + (x^{2} y + 2 x) d y = 0$
71041	Solve the Differential Equation	(dy)/(dx)=4x-7	$\frac{d y}{d x} = 4 x - 7$
71042	Solve the Differential Equation	(dy)/(dx)+y/x=x^2y^2	$\frac{d y}{d x} + \frac{y}{x} = x^{2} y^{2}$
71043	Solve the Differential Equation	(dy)/(dx)-5y=0	$\frac{d y}{d x} - 5 y = 0$
71044	Solve the Differential Equation	4y''''''''+y''''=0	$4 y'''' + y'' = 0$
71045	Solve the Differential Equation	(dy)/(dx)=(5y)/x	$\frac{d y}{d x} = \frac{5 y}{x}$
71046	Solve the Differential Equation	y''''=x-4xy	$y'' = x - 4 x y$
71047	Solve the Differential Equation	y''''+y=y^-2	$y'' + y = y^{- 2}$
71048	Solve the Differential Equation	(x+y)dy=(x-y)dx	$(x + y) d y = (x - y) d x$
71049	Solve the Differential Equation	(1+x)(dy)/(dx)-xy=x+x^2	$(1 + x) \frac{d y}{d x} - x y = x + x^{2}$
71050	Solve the Differential Equation	(dy)/(dt)=21t^2	$\frac{d y}{d t} = 21 t^{2}$
71051	Solve the Differential Equation	-(yd)x+(x+ square root of xy)dy=0	$- yd x + (x + \sqrt{x y}) d y = 0$
71052	Solve the Differential Equation	t(dy)/(dt)-y=2t^3	$t \frac{d y}{d t} - y = 2 t^{3}$
71053	Solve the Differential Equation	(dy)/(dx)=2x-4	$\frac{d y}{d x} = 2 x - 4$
71054	Solve the Differential Equation	xdx-y^2dy=0	$x d x - y^{2} d y = 0$
71055	Solve the Differential Equation	6x(yd)x+(4y+9y^2)dy=0	$6 x yd x + (4 y + 9 y^{2}) d y = 0$
71056	Solve the Differential Equation	(dy)/(dx)=x^2+1	$\frac{d y}{d x} = x^{2} + 1$
71057	Solve the Differential Equation	(dy)/(dx)+2xy=x	$\frac{d y}{d x} + 2 x y = x$
71058	Solve the Differential Equation	(dy)/(dx)=(x+1)/y	$\frac{d y}{d x} = \frac{x + 1}{y}$
71059	Solve the Differential Equation	(dy)/(dt)=21t^6	$\frac{d y}{d t} = 21 t^{6}$
71060	Solve the Differential Equation	2x(yd)x+(x^2-1)dy=0	$2 x yd x + (x^{2} - 1) d y = 0$
71061	Solve the Differential Equation	x(dy)/(dx)+y=(x^2+3x)e^(2/3x)	$x \frac{d y}{d x} + y = (x^{2} + 3 x) e^{\frac{2}{3} x}$
71062	Solve the Differential Equation	xy''''-y=0	$x y'' - y = 0$
71063	Solve the Differential Equation	(dy)/(dx)=ysin(x)	$\frac{d y}{d x} = y \sin (x)$
71064	Solve the Differential Equation	(x^2+y^2+1)dx+x(x-2y)dy=0	$(x^{2} + y^{2} + 1) d x + x (x - 2 y) d y = 0$
71065	Solve the Differential Equation	(dy)/(dt)=27t^2	$\frac{d y}{d t} = 27 t^{2}$
71066	Solve the Differential Equation	(dy)/(dx)=5xy	$\frac{d y}{d x} = 5 x y$
71067	Solve the Differential Equation	(dr)/(dtheta)=(r^2)/theta	$\frac{d r}{d θ} = \frac{r^{2}}{θ}$
71068	Solve the Differential Equation	(dy)/(dx)=((x-1)y^5)/(x^2(2y^3-y))	$\frac{d y}{d x} = \frac{(x - 1) y^{5}}{x^{2} (2 y^{3} - y)}$
71069	Solve the Differential Equation	(dy)/(dx)=(y^2)/x	$\frac{d y}{d x} = \frac{y^{2}}{x}$
71070	Solve the Differential Equation	(dy)/(dx)=-2y	$\frac{d y}{d x} = - 2 y$
71071	Solve the Differential Equation	(dy)/(dx)=6x-3y	$\frac{d y}{d x} = 6 x - 3 y$
71072	Solve the Differential Equation	(dy)/(dt)=25t^4	$\frac{d y}{d t} = 25 t^{4}$
71073	Solve the Differential Equation	1/xdx-1/ydy=0	$\frac{1}{x} d x - \frac{1}{y} d y = 0$
71074	Solve the Differential Equation	y''''-3/xy=x^4	$y'' - \frac{3}{x} y = x^{4}$
71075	Solve the Differential Equation	(dy)/(dx)-2y=y^2 ; , y(0)=3	$\frac{d y}{d x} - 2 y = y^{2}$ ; , $y (0) = 3$
71076	Solve the Differential Equation	(dy)/(dx)=3x^2-1	$\frac{d y}{d x} = 3 x^{2} - 1$
71077	Solve the Differential Equation	(dy)/(dx)+y=e^(2x)	$\frac{d y}{d x} + y = e^{2 x}$
71078	Solve the Differential Equation	(dy)/(dx)=3x-7	$\frac{d y}{d x} = 3 x - 7$
71079	Solve the Differential Equation	(dy)/(dx)-y=xy^2	$\frac{d y}{d x} - y = x y^{2}$
71080	Solve the Differential Equation	(dy)/(dt)=35t^6	$\frac{d y}{d t} = 35 t^{6}$
71081	Solve the Differential Equation	(dy)/(dx)=(y+x)/x	$\frac{d y}{d x} = \frac{y + x}{x}$
71082	Solve the Differential Equation	ydx=(x+ square root of y^2-x^2)dy	$yd x = (x + \sqrt{y^{2} - x^{2}}) d y$
71083	Solve the Differential Equation	xy''''=y+x/(x+1)	$x y'' = y + \frac{x}{x + 1}$
71084	Solve the Differential Equation	(dy)/(dx)=(x^2+2)/y	$\frac{d y}{d x} = \frac{x^{2} + 2}{y}$
71085	Solve the Differential Equation	(dy)/(dt)=27t^8	$\frac{d y}{d t} = 27 t^{8}$
71086	Solve the Differential Equation	(dy)/(dx)=(x+1)/(e^y)	$\frac{d y}{d x} = \frac{x + 1}{e^{y}}$
71087	Solve the Differential Equation	x^2(dy)/(dx)-2xy=3y^4	$x^{2} \frac{d y}{d x} - 2 x y = 3 y^{4}$
71088	Solve the Differential Equation	(dx)/(dt)=x^2-2x+2	$\frac{d x}{d t} = x^{2} - 2 x + 2$
71089	Solve the Differential Equation	(dy)/(dx)=3x^2y-2xy	$\frac{d y}{d x} = 3 x^{2} y - 2 x y$
71090	Solve the Differential Equation	(dy)/(dx)+e^(x-y)=0	$\frac{d y}{d x} + e^{x - y} = 0$
71091	Solve the Differential Equation	(dy)/(dx)+Py=0	$\frac{d y}{d x} + P y = 0$
71092	Solve the Differential Equation	(dy)/(dx)=3xy	$\frac{d y}{d x} = 3 x y$
71093	Solve the Differential Equation	(dy)/(dx)-3y=0	$\frac{d y}{d x} - 3 y = 0$
71094	Solve the Differential Equation	(e^x+2xy^2)dx+2x^2(yd)y=0	$(e^{x} + 2 x y^{2}) d x + 2 x^{2} yd y = 0$
71095	Solve the Differential Equation	xy''''''''+y''''=0	$x y'''' + y'' = 0$
71096	Solve the Differential Equation	(dy)/(dx)=x^3+2x	$\frac{d y}{d x} = x^{3} + 2 x$
71097	Solve the Differential Equation	xy''''-2y=x^2	$x y'' - 2 y = x^{2}$
71098	Solve the Differential Equation	(dy)/(dx)+y=x	$\frac{d y}{d x} + y = x$
71099	Solve the Differential Equation	(x^2+1)y''''-2xy-2x=0	$(x^{2} + 1) y'' - 2 x y - 2 x = 0$
71100	Solve the Differential Equation	y''''=2x	$y'' = 2 x$