Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72701	Solve the Differential Equation	(d^2y)/(dx^2)=0	$\frac{d^{2} y}{d x^{2}} = 0$
72702	Solve the Differential Equation	x(1+y^2)^(1/2)dx=y(1+x^2)^(1/2)dy	$x {(1 + y^{2})}^{\frac{1}{2}} d x = y {(1 + x^{2})}^{\frac{1}{2}} d y$
72703	Solve the Differential Equation	(y^2-x^2)dx+x(yd)y=0	$(y^{2} - x^{2}) d x + x yd y = 0$
72704	Solve the Differential Equation	(dr)/(dtheta)=pisin(pitheta) , r(0)=3	$\frac{d r}{d θ} = π \sin (π θ)$ , $r (0) = 3$
72705	Solve the Differential Equation	x^2(dy)/(dx)+2xy = natural log of x , y(1)=2	$x^{2} \frac{d y}{d x} + 2 x y = \ln (x)$ , $y (1) = 2$
72706	Solve the Differential Equation	(dy)/(dx)=cos(4x)-2x	$\frac{d y}{d x} = \cos (4 x) - 2 x$
72707	Solve the Differential Equation	(dy)/(dx)+ycos(x)=5cos(x)	$\frac{d y}{d x} + y \cos (x) = 5 \cos (x)$
72708	Solve the Differential Equation	(x+1)y''''=xy	$(x + 1) y'' = x y$
72709	Solve the Differential Equation	(dy)/(dx)=(-2x)/y	$\frac{d y}{d x} = \frac{- 2 x}{y}$
72710	Solve the Differential Equation	dx-(y-2xy)dy=0	$d x - (y - 2 x y) d y = 0$
72711	Solve the Differential Equation	(dy)/(dx)=y^2x^4-y^2+x^4-1	$\frac{d y}{d x} = y^{2} x^{4} - y^{2} + x^{4} - 1$
72712	Solve the Differential Equation	(ds)/(dt)=20t(5t^2-3)^3 , s(1)=3	$\frac{d s}{d t} = 20 t {(5 t^{2} - 3)}^{3}$ , $s (1) = 3$
72713	Solve the Differential Equation	(3x^2+1)y''''=6xy	$(3 x^{2} + 1) y'' = 6 x y$
72714	Solve the Differential Equation	4+x^2=(1-y^5)(dy)/(dx)	$4 + x^{2} = (1 - y^{5}) \frac{d y}{d x}$
72715	Solve the Differential Equation	(dy)/(dx)=(38x)/(e^y)	$\frac{d y}{d x} = \frac{38 x}{e^{y}}$
72716	Solve the Differential Equation	(dy)/(dx)=3y+6	$\frac{d y}{d x} = 3 y + 6$
72717	Solve the Differential Equation	(dy)/(dx)=(x+1)/(y-1)	$\frac{d y}{d x} = \frac{x + 1}{y - 1}$
72718	Solve the Differential Equation	(dy)/(dx)=-0.4y	$\frac{d y}{d x} = - 0.4 y$
72719	Solve the Differential Equation	(dy)/(dx)=e^(x-y)+x^2e^(-y)	$\frac{d y}{d x} = e^{x - y} + x^{2} e^{- y}$
72720	Solve the Differential Equation	(dy)/(dx)=-2x+9x^2	$\frac{d y}{d x} = - 2 x + 9 x^{2}$
72721	Solve the Differential Equation	(dy)/(dx)=-(xe^(-x^2))/y	$\frac{d y}{d x} = - \frac{x e^{- x^{2}}}{y}$
72722	Solve the Differential Equation	(-3x+y+6)dx+(x+y+2)dy=0	$(- 3 x + y + 6) d x + (x + y + 2) d y = 0$
72723	Solve the Differential Equation	(dy)/(dx)+20y=24	$\frac{d y}{d x} + 20 y = 24$
72724	Solve the Differential Equation	(dr)/(dt)=-4rt	$\frac{d r}{d t} = - 4 r t$
72725	Solve the Differential Equation	(dy)/(dx)=(13x)/y	$\frac{d y}{d x} = \frac{13 x}{y}$
72726	Solve the Differential Equation	(dy)/(dx)=12x	$\frac{d y}{d x} = 12 x$
72727	Solve the Differential Equation	y^2+x^2y''''=xyy''''	$y^{2} + x^{2} y'' = x y y''$
72728	Solve the Differential Equation	(y-x+xycot(x))dx+xdy=0	$(y - x + x y \cot (x)) d x + x d y = 0$
72729	Solve the Differential Equation	(x+1)(dy)/(dx)+y = natural log of x	$(x + 1) \frac{d y}{d x} + y = \ln (x)$
72730	Solve the Differential Equation	(x^2+y^2+1)dx+(x^2-2xy)dy=0	$(x^{2} + y^{2} + 1) d x + (x^{2} - 2 x y) d y = 0$
72731	Solve the Differential Equation	xy''''-4y=x^6e^x	$x y'' - 4 y = x^{6} e^{x}$
72732	Solve the Differential Equation	(dy)/(dx)=4e^(3x)	$\frac{d y}{d x} = 4 e^{3 x}$
72733	Solve the Differential Equation	x^2y''''-2xy=x^4+3	$x^{2} y'' - 2 x y = x^{4} + 3$
72734	Solve the Differential Equation	2(yd)y=(x^2+1)dx	$2 yd y = (x^{2} + 1) d x$
72735	Solve the Differential Equation	cos(x)(dy)/(dx)+ysin(x)=sin(x)cos(x)	$\cos (x) \frac{d y}{d x} + y \sin (x) = \sin (x) \cos (x)$
72736	Solve the Differential Equation	solve the differential equation of (dy)/(dx)=4cos(6x)	solve the differential equation of $\frac{d y}{d x} = 4 \cos (6 x)$
72737	Solve the Differential Equation	(dy)/(dx)=6x^2y	$\frac{d y}{d x} = 6 x^{2} y$
72738	Solve the Differential Equation	(dy)/(dx)=xe^(x^2)	$\frac{d y}{d x} = x e^{x^{2}}$
72739	Solve the Differential Equation	(dy)/(dx)=(x^5)/y	$\frac{d y}{d x} = \frac{x^{5}}{y}$
72740	Solve the Differential Equation	f(x)=5	$f (x) = 5$
72741	Solve the Differential Equation	(2y^2+3xy-2y+6x)dx+x(x+2y-1)dy=0	$(2 y^{2} + 3 x y - 2 y + 6 x) d x + x (x + 2 y - 1) d y = 0$
72742	Solve the Differential Equation	(dy)/(dx)=-0.5y	$\frac{d y}{d x} = - 0.5 y$
72743	Solve the Differential Equation	(2x+y+1)y''''=1	$(2 x + y + 1) y'' = 1$
72744	Solve the Differential Equation	(2x+6x^2y)dx+(3x^3-2xy)dy=0	$(2 x + 6 x^{2} y) d x + (3 x^{3} - 2 x y) d y = 0$
72745	Solve the Differential Equation	y''''=(3y)/x	$y'' = \frac{3 y}{x}$
72746	Solve the Differential Equation	(xy+x^2y^3)y''''=1	$(x y + x^{2} y^{3}) y'' = 1$
72747	Solve the Differential Equation	(dy)/(dx)=4x^3-6x^2+x	$\frac{d y}{d x} = 4 x^{3} - 6 x^{2} + x$
72748	Solve the Differential Equation	(dy)/(dx)=(34x)/(e^y)	$\frac{d y}{d x} = \frac{34 x}{e^{y}}$
72749	Solve the Differential Equation	x^2dy+(xy+x^2)dx=0	$x^{2} d y + (x y + x^{2}) d x = 0$
72750	Solve the Differential Equation	(dy)/(dx)=e^(0.05x)	$\frac{d y}{d x} = e^{0.05 x}$
72751	Solve the Differential Equation	2x^2dy-(y^2+2xy-x^2)dx=0	$2 x^{2} d y - (y^{2} + 2 x y - x^{2}) d x = 0$
72752	Solve the Differential Equation	(dy)/(dx)=4e^(-4x)	$\frac{d y}{d x} = 4 e^{- 4 x}$
72753	Solve the Differential Equation	(dy)/(dt)+y=e^(-t)	$\frac{d y}{d t} + y = e^{- t}$
72754	Solve the Differential Equation	y''''=x+5y	$y'' = x + 5 y$
72755	Solve the Differential Equation	(dy)/(dx)=2cos(2x)	$\frac{d y}{d x} = 2 \cos (2 x)$
72756	Solve the Differential Equation	(dy)/(dx)=x^2-1	$\frac{d y}{d x} = x^{2} - 1$
72757	Solve the Differential Equation	(dy)/(dx)=(1+y^2)/x	$\frac{d y}{d x} = \frac{1 + y^{2}}{x}$
72758	Solve the Differential Equation	(dy)/(dx)=-x/(2y)	$\frac{d y}{d x} = - \frac{x}{2 y}$
72759	Solve the Differential Equation	xy^2y''''=x+2	$x y^{2} y'' = x + 2$
72760	Solve the Differential Equation	(dy)/(dx)=(3y^2)/(cos(pix))	$\frac{d y}{d x} = \frac{3 y^{2}}{\cos (π x)}$
72761	Solve the Differential Equation	(x+2y)dx-3(yd)y=0	$(x + 2 y) d x - 3 yd y = 0$
72762	Solve the Differential Equation	(dy)/(dx)=(3x+2)/(y^2-1)	$\frac{d y}{d x} = \frac{3 x + 2}{y^{2} - 1}$
72763	Solve the Differential Equation	xy(dy)/(dx) = natural log of x	$x y \frac{d y}{d x} = \ln (x)$
72764	Solve the Differential Equation	(xy-1)dx+(x^2-xy)dy=0	$(x y - 1) d x + (x^{2} - x y) d y = 0$
72765	Solve the Differential Equation	(dy)/(dx)=(x^2y^3)/(x+3)	$\frac{d y}{d x} = \frac{x^{2} y^{3}}{x + 3}$
72766	Solve the Differential Equation	(dy)/(dx)=(2e^x)/(e^y)	$\frac{d y}{d x} = \frac{2 e^{x}}{e^{y}}$
72767	Solve the Differential Equation	(xy+y+y^2)dx+(x+2y)dy=0	$(x y + y + y^{2}) d x + (x + 2 y) d y = 0$
72768	Solve the Differential Equation	x^2dy+y^2dx=0	$x^{2} d y + y^{2} d x = 0$
72769	Solve the Differential Equation	(dy)/(dx)=11e^(x-y)	$\frac{d y}{d x} = 11 e^{x - y}$
72770	Solve the Differential Equation	(dy)/(dx)=(4y)/(x(y-3))	$\frac{d y}{d x} = \frac{4 y}{x (y - 3)}$
72771	Solve the Differential Equation	x(x+y)dy=(x^2+y^2)dy	$x (x + y) d y = (x^{2} + y^{2}) d y$
72772	Solve the Differential Equation	(dy)/(dx)=38x	$\frac{d y}{d x} = 38 x$
72773	Solve the Differential Equation	(dx)/(dt)=kx	$\frac{d x}{d t} = k x$
72774	Solve the Differential Equation	y''''+2xy=xe^(-x^2)	$y'' + 2 x y = x e^{- x^{2}}$
72775	Solve the Differential Equation	(4x^3y-15x^2-y)dx+(x^4+3y^2-x)dy=0	$(4 x^{3} y - 15 x^{2} - y) d x + (x^{4} + 3 y^{2} - x) d y = 0$
72776	Solve the Differential Equation	(dy)/(dx)=xe^(2y)	$\frac{d y}{d x} = x e^{2 y}$
72777	Solve the Differential Equation	(dy)/(dx)=sin(5*x)	$\frac{d y}{d x} = \sin (5 \cdot x)$
72778	Solve the Differential Equation	(x^2+1)(dy)/(dx)+4xy=x , y(2)=1	$(x^{2} + 1) \frac{d y}{d x} + 4 x y = x$ , $y (2) = 1$
72779	Solve the Differential Equation	y''''''''''''''''+2y''''''''+y=0	$y'''''''' + 2 y'''' + y = 0$
72780	Solve the Differential Equation	xsin(y/x)(dy)/(dx)+x-ysin(y/x)=0	$x \sin (\frac{y}{x}) \frac{d y}{d x} + x - y \sin (\frac{y}{x}) = 0$
72781	Solve the Differential Equation	ydy=xdx	$yd y = x d x$
72782	Solve the Differential Equation	y''''-y=xy^5	$y'' - y = x y^{5}$
72783	Solve the Differential Equation	xdy-(yd)x = square root of x^2+y^2dx	$x d y - yd x = \sqrt{x^{2} + y^{2}} d x$
72784	Solve the Differential Equation	(dy)/(dx)+1/xy=2	$\frac{d y}{d x} + \frac{1}{x} y = 2$
72785	Solve the Differential Equation	square root of x(dy)/(dx)=e^(4y+ square root of x)	$\sqrt{x} \frac{d y}{d x} = e^{4 y + \sqrt{x}}$
72786	Solve the Differential Equation	(dx)/(dt)=4(x^2+1) , x(pi/4)=1	$\frac{d x}{d t} = 4 (x^{2} + 1)$ , $x (\frac{π}{4}) = 1$
72787	Solve the Differential Equation	f(x) = square root of x+5	$f (x) = \sqrt{x + 5}$
72788	Solve the Differential Equation	(dh)/(dt)=(17.6t)/( square root of 17.6t^2+1)	$\frac{d h}{d t} = \frac{17.6 t}{\sqrt{17.6 t^{2} + 1}}$
72789	Solve the Differential Equation	square root of 1-4x^2y''''=x	$\sqrt{1 - 4 x^{2}} y'' = x$
72790	Solve the Differential Equation	x^2y''''''''-3xy''''+4y=0	$x^{2} y'''' - 3 x y'' + 4 y = 0$
72791	Solve the Differential Equation	(x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0	$(x^{3} + x y^{2} - y) d x + (y^{3} + x^{2} y + x) d y = 0$
72792	Solve the Differential Equation	(2x+3)(dy)/(dx)=y+(2x+3)^(1/2)	$(2 x + 3) \frac{d y}{d x} = y + {(2 x + 3)}^{\frac{1}{2}}$
72793	Solve the Differential Equation	(dy)/(dx)=(y-1)^2	$\frac{d y}{d x} = {(y - 1)}^{2}$
72794	Solve the Differential Equation	y''''+3y=x+e^(-2x)	$y'' + 3 y = x + e^{- 2 x}$
72795	Solve the Differential Equation	(dy)/(dx)=2 square root of y	$\frac{d y}{d x} = 2 \sqrt{y}$
72796	Solve the Differential Equation	y''''=y/(x+y)	$y'' = \frac{y}{x + y}$
72797	Solve the Differential Equation	(dy)/(dx) para y = square root of x^3+x	$\frac{d y}{d x}$ para $y = \sqrt{x^{3} + x}$
72798	Solve the Differential Equation	xdy=(y-x)dx	$x d y = (y - x) d x$
72799	Solve the Differential Equation	(x^2+y^2)dx+(xy)dy=0	$(x^{2} + y^{2}) d x + (x y) d y = 0$
72800	Solve the Differential Equation	3(dy)/(dx)+3/xy=2x^4y^4	$3 \frac{d y}{d x} + \frac{3}{x} y = 2 x^{4} y^{4}$