Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
73901	Solve the Differential Equation	(y+x^3y^3)dx+xdy=0	$(y + x^{3} y^{3}) d x + x d y = 0$
73902	Solve the Differential Equation	(dy)/(dx)=3e^x	$\frac{d y}{d x} = 3 e^{x}$
73903	Solve the Differential Equation	2x^2dy=(2xy+y^2)dx	$2 x^{2} d y = (2 x y + y^{2}) d x$
73904	Solve the Differential Equation	y''''+xy=x	$y'' + x y = x$
73905	Solve the Differential Equation	3y''''''''+2y''''+y=0	$3 y'''' + 2 y'' + y = 0$
73906	Solve the Differential Equation	(d^2y)/(dx^2)=-1/(x^3)	$\frac{d^{2} y}{d x^{2}} = - \frac{1}{x^{3}}$
73907	Solve the Differential Equation	(dy)/(dx)=(xsin(x))/y	$\frac{d y}{d x} = \frac{x \sin (x)}{y}$
73908	Solve the Differential Equation	(dy)/(dx)=e^(2x)+y-1	$\frac{d y}{d x} = e^{2 x} + y - 1$
73909	Solve the Differential Equation	xdy-(yd)x=0	$x d y - yd x = 0$
73910	Solve the Differential Equation	y''''=cos(x-y)	$y'' = \cos (x - y)$
73911	Solve the Differential Equation	(dy)/(dx)+y=2e^x	$\frac{d y}{d x} + y = 2 e^{x}$
73912	Solve the Differential Equation	x(dy)/(dx)=y+xe^(y/x)	$x \frac{d y}{d x} = y + x e^{\frac{y}{x}}$
73913	Solve the Differential Equation	x^2y''''-2y=0	$x^{2} y'' - 2 y = 0$
73914	Solve the Differential Equation	(x^5-y^2)dx+2x(yd)y=0	$(x^{5} - y^{2}) d x + 2 x yd y = 0$
73915	Solve the Differential Equation	(dy)/(dt)=6y	$\frac{d y}{d t} = 6 y$
73916	Solve the Differential Equation	cos(x)^2sin(xdy)+(ycos(x)^3-1)dx=0	$\cos^{2} (x) \sin (x d y) + (y \cos^{3} (x) - 1) d x = 0$
73917	Solve the Differential Equation	xy''''+y=4x	$x y'' + y = 4 x$
73918	Solve the Differential Equation	(dP)/(dt)=k square root of t	$\frac{d P}{d t} = k \sqrt{t}$
73919	Solve the Differential Equation	x^2y''''''''+xy''''-y=1/(x+1)	$x^{2} y'''' + x y'' - y = \frac{1}{x + 1}$
73920	Solve the Differential Equation	3x(dy)/(dx)=5-x^3	$3 x \frac{d y}{d x} = 5 - x^{3}$
73921	Solve the Differential Equation	(dy)/(dx)=(x+2)/y	$\frac{d y}{d x} = \frac{x + 2}{y}$
73922	Solve the Differential Equation	4(5)(dy)/(dt)+4(-1)(-8)-3*-8+15(-1)^2(dy)/(dt)=0	$4 (5) \frac{d y}{d t} + 4 (- 1) (- 8) - 3 \cdot - 8 + 15 {(- 1)}^{2} \frac{d y}{d t} = 0$
73923	Solve the Differential Equation	y''''-2xy+x=0	$y'' - 2 x y + x = 0$
73924	Solve the Differential Equation	f(x)=4/3 square root of x^3	$f (x) = \frac{4}{3} \sqrt{x^{3}}$
73925	Solve the Differential Equation	(ds)/(dt)=28t(7t^2-5)^3 , s(1)=11	$\frac{d s}{d t} = 28 t {(7 t^{2} - 5)}^{3}$ , $s (1) = 11$
73926	Solve the Differential Equation	(dy)/(dx)=3(16+y^2)-2xy	$\frac{d y}{d x} = 3 (16 + y^{2}) - 2 x y$
73927	Solve the Differential Equation	x^2(dy)/(dx)+xy=2	$x^{2} \frac{d y}{d x} + x y = 2$
73928	Solve the Differential Equation	y''''=xe^(2y)	$y'' = x e^{2 y}$
73929	Solve the Differential Equation	y''''=e^(2x-1)y^2	$y'' = e^{2 x - 1} y^{2}$
73930	Solve the Differential Equation	f(x)=2x^2	$f (x) = 2 x^{2}$
73931	Solve the Differential Equation	(dy)/(dx)-3/xy=x^4	$\frac{d y}{d x} - \frac{3}{x} y = x^{4}$
73932	Solve the Differential Equation	y''''''''-4y''''+8y=0	$y'''' - 4 y'' + 8 y = 0$
73933	Solve the Differential Equation	(dy)/(dx)+ycos(x)=3cos(x)	$\frac{d y}{d x} + y \cos (x) = 3 \cos (x)$
73934	Solve the Differential Equation	(2y^2+3x)dx+(2xy)dy=0	$(2 y^{2} + 3 x) d x + (2 x y) d y = 0$
73935	Solve the Differential Equation	(dy)/(dx)=e^(x-2y)	$\frac{d y}{d x} = e^{x - 2 y}$
73936	Solve the Differential Equation	(dy)/(dx)=18x^2-8x	$\frac{d y}{d x} = 18 x^{2} - 8 x$
73937	Solve the Differential Equation	(dP)/(dy)+AyP=0	$\frac{d P}{d y} + A y P = 0$
73938	Solve the Differential Equation	4x^3y+x^4y''''=sin(x)^3	$4 x^{3} y + x^{4} y'' = \sin^{3} (x)$
73939	Solve the Differential Equation	yy''''''''+(y'''')^2=0	$y y'''' + {(y'')}^{2} = 0$
73940	Solve the Differential Equation	(dy)/(dx)=(y^2+xy(1+e^(x/y)))/(x^2(1+e^(x/y)))	$\frac{d y}{d x} = \frac{y^{2} + x y (1 + e^{\frac{x}{y}})}{x^{2} (1 + e^{\frac{x}{y}})}$
73941	Solve the Differential Equation	(dy)/(dt)=-1/50(y-19)	$\frac{d y}{d t} = - \frac{1}{50} (y - 19)$
73942	Solve the Differential Equation	(dy)/(dx)=3x^2-3	$\frac{d y}{d x} = 3 x^{2} - 3$
73943	Solve the Differential Equation	7 square root of xy(dy)/(dx)=1	$7 \sqrt{x y} \frac{d y}{d x} = 1$
73944	Solve the Differential Equation	(dy)/(dt)=k cube root of t	$\frac{d y}{d t} = k \sqrt[3]{t}$
73945	Solve the Differential Equation	(d^2y)/(dx^2)=48x^2	$\frac{d^{2} y}{d x^{2}} = 48 x^{2}$
73946	Solve the Differential Equation	(ds)/(dt)=8sin(t-pi/12)^2 , s(0)=8	$\frac{d s}{d t} = 8 \sin^{2} (t - \frac{π}{12})$ , $s (0) = 8$
73947	Solve the Differential Equation	(dz)/(dx)=9x^2-9x	$\frac{d z}{d x} = 9 x^{2} - 9 x$
73948	Solve the Differential Equation	5y(dy)/(dx)=2x^2	$5 y \frac{d y}{d x} = 2 x^{2}$
73949	Solve the Differential Equation	y''''=8x+e^(2x)	$y'' = 8 x + e^{2 x}$
73950	Solve the Differential Equation	(dy)/(dx)=-7x^3-3x	$\frac{d y}{d x} = - 7 x^{3} - 3 x$
73951	Solve the Differential Equation	2xy^2+4=2(3-x^2y)(dy)/(dx)	$2 x y^{2} + 4 = 2 (3 - x^{2} y) \frac{d y}{d x}$
73952	Solve the Differential Equation	(x^2+y^2)(dy)/(dx)=xy	$(x^{2} + y^{2}) \frac{d y}{d x} = x y$
73953	Solve the Differential Equation	2(dy)/(dx)+y=0	$2 \frac{d y}{d x} + y = 0$
73954	Solve the Differential Equation	dy+y/xdx=3x^2y^2dx	$d y + \frac{y}{x} d x = 3 x^{2} y^{2} d x$
73955	Solve the Differential Equation	(d^2y)/(dx^2)=54x	$\frac{d^{2} y}{d x^{2}} = 54 x$
73956	Solve the Differential Equation	(1/y-x/y)dx+(x^2cos(y))dy=0	$(\frac{1}{y} - \frac{x}{y}) d x + (x^{2} \cos (y)) d y = 0$
73957	Solve the Differential Equation	(dy)/(dx)-y^2+6y=13	$\frac{d y}{d x} - y^{2} + 6 y = 13$
73958	Solve the Differential Equation	(ds)/(dt)=28t(7t^2-5)^3 , s(1)=1	$\frac{d s}{d t} = 28 t {(7 t^{2} - 5)}^{3}$ , $s (1) = 1$
73959	Solve the Differential Equation	(dy)/(dx)-y/x=xe^x	$\frac{d y}{d x} - \frac{y}{x} = x e^{x}$
73960	Solve the Differential Equation	square root of 1+x^3(dy)/(dx)=x^2y+x^2	$\sqrt{1 + x^{3}} \frac{d y}{d x} = x^{2} y + x^{2}$
73961	Solve the Differential Equation	x(yd)y-(x^2+2)dx=0	$x yd y - (x^{2} + 2) d x = 0$
73962	Solve the Differential Equation	(dy)/(dx)=tan(x)+sec(x)	$\frac{d y}{d x} = \tan (x) + \sec (x)$
73963	Solve the Differential Equation	(x^2+y^2)dx+(2xy)dy=0	$(x^{2} + y^{2}) d x + (2 x y) d y = 0$
73964	Solve the Differential Equation	(dy)/(dx)+2e^xy=e^x	$\frac{d y}{d x} + 2 e^{x} y = e^{x}$
73965	Solve the Differential Equation	1/x(dy)/(dx)+y=1	$\frac{1}{x} \cdot \frac{d y}{d x} + y = 1$
73966	Solve the Differential Equation	(dx)/(dt)=-4xt	$\frac{d x}{d t} = - 4 x t$
73967	Solve the Differential Equation	(dy)/(dx)+2y=6	$\frac{d y}{d x} + 2 y = 6$
73968	Solve the Differential Equation	dx=y/(1-x^2y^2)dx+x/(1-x^2y^2)dy	$d x = \frac{y}{1 - x^{2} y^{2}} d x + \frac{x}{1 - x^{2} y^{2}} d y$
73969	Solve the Differential Equation	(dy)/(dt)=16t^7	$\frac{d y}{d t} = 16 t^{7}$
73970	Solve the Differential Equation	t(dy)/(dt)-5t=-y	$t \frac{d y}{d t} - 5 t = - y$
73971	Solve the Differential Equation	(d^2y)/(dx^2)+(dy)/(dx)=0	$\frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} = 0$
73972	Solve the Differential Equation	y^2dy=x(xdy-(yd)x)e^(x/y)	$y^{2} d y = x (x d y - yd x) e^{\frac{x}{y}}$
73973	Solve the Differential Equation	(dy)/(dx)=(x^3+2)y	$\frac{d y}{d x} = (x^{3} + 2) y$
73974	Solve the Differential Equation	f(x)=x^7(5+8x)^3	$f (x) = x^{7} {(5 + 8 x)}^{3}$
73975	Solve the Differential Equation	((dy)/(dx))+y=e^(3x)	$(\frac{d y}{d x}) + y = e^{3 x}$
73976	Solve the Differential Equation	y''''-4y''''+13y=0	$y'' - 4 y'' + 13 y = 0$
73977	Solve the Differential Equation	1/ydy=1/(x^2)dx	$\frac{1}{y} d y = \frac{1}{x^{2}} d x$
73978	Solve the Differential Equation	(dy)/(dx)=xy^(1/3)	$\frac{d y}{d x} = x y^{\frac{1}{3}}$
73979	Solve the Differential Equation	(dy)/(dx)-y=1	$\frac{d y}{d x} - y = 1$
73980	Solve the Differential Equation	(dy)/(dx)=1/( square root of 4x-3)	$\frac{d y}{d x} = \frac{1}{\sqrt{4 x - 3}}$
73981	Solve the Differential Equation	(dy)/(dx)+y/(2x)=x/(y^3)	$\frac{d y}{d x} + \frac{y}{2 x} = \frac{x}{y^{3}}$
73982	Solve the Differential Equation	xy''''+xy=1-y	$x y'' + x y = 1 - y$
73983	Solve the Differential Equation	dy+dx=0	$d y + d x = 0$
73984	Solve the Differential Equation	(dy)/(dx)=(1+4x) square root of y	$\frac{d y}{d x} = (1 + 4 x) \sqrt{y}$
73985	Solve the Differential Equation	2xdy+ydx=8x^3dx	$2 x d y + yd x = 8 x^{3} d x$
73986	Solve the Differential Equation	(dr)/(dtheta)=pisin(pitheta) , r(1)=2	$\frac{d r}{d θ} = π \sin (π θ)$ , $r (1) = 2$
73987	Solve the Differential Equation	((d^2y)/(dx^2))^3+((dy)/(dx))^4+y=0	${(\frac{d^{2} y}{d x^{2}})}^{3} + {(\frac{d y}{d x})}^{4} + y = 0$
73988	Solve the Differential Equation	xdy+ydx+xy(3dx+dy)=0	$x d y + yd x + x y (3 d x + d y) = 0$
73989	Solve the Differential Equation	(dy)/(dx)=7x^-3+5x^-1-1 ; , y(1)=3	$\frac{d y}{d x} = 7 x^{- 3} + 5 x^{- 1} - 1$ ; , $y (1) = 3$
73990	Solve the Differential Equation	sin(y)(x+sin(y))dx+2x^2cos(ydy)=0	$\sin (y) (x + \sin (y)) d x + 2 x^{2} \cos (yd y) = 0$
73991	Solve the Differential Equation	xy''''-2y=3x^2+2x	$x y'' - 2 y = 3 x^{2} + 2 x$
73992	Solve the Differential Equation	xy''''+5y=7x^2	$x y'' + 5 y = 7 x^{2}$
73993	Solve the Differential Equation	(d^2y)/(dx^2)+(dy)/(dx)-12y=5x+8	$\frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} - 12 y = 5 x + 8$
73994	Solve the Differential Equation	y''''=(-2y)/x	$y'' = \frac{- 2 y}{x}$
73995	Solve the Differential Equation	(dv)/(dt)=4/(1+t^2)+sec(t)^2 , v(0)=1	$\frac{d v}{d t} = \frac{4}{1 + t^{2}} + \sec^{2} (t)$ , $v (0) = 1$
73996	Solve the Differential Equation	(dy)/(dx)=(14x)/(e^y)	$\frac{d y}{d x} = \frac{14 x}{e^{y}}$
73997	Solve the Differential Equation	xdy=ydx	$x d y = yd x$
73998	Solve the Differential Equation	3y''''-y''''=0	$3 y'' - y'' = 0$
73999	Solve the Differential Equation	y''''=(y(y-2))/(x(y-1))	$y'' = \frac{y (y - 2)}{x (y - 1)}$
74000	Solve the Differential Equation	(dy)/(dx)=y/x+2x	$\frac{d y}{d x} = \frac{y}{x} + 2 x$