Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72101	Solve the Differential Equation	(dy)/(dx)=1/11 square root of ycos( square root of y)^2	$\frac{d y}{d x} = \frac{1}{11} \sqrt{y} \cos^{2} (\sqrt{y})$
72102	Solve the Differential Equation	(dy)/(dt)=cos(t) , y(pi/2)=2	$\frac{d y}{d t} = \cos (t)$ , $y (\frac{π}{2}) = 2$
72103	Solve the Differential Equation	(dy)/(dx)=-0.2y	$\frac{d y}{d x} = - 0.2 y$
72104	Solve the Differential Equation	(dy)/(dx)=(x+3x^2)/(y^2)	$\frac{d y}{d x} = \frac{x + 3 x^{2}}{y^{2}}$
72105	Solve the Differential Equation	xdx+(x^2y+4y)dy=0	$x d x + (x^{2} y + 4 y) d y = 0$
72106	Solve the Differential Equation	(dy)/(dx)=(x+3y)/(2x)	$\frac{d y}{d x} = \frac{x + 3 y}{2 x}$
72107	Solve the Differential Equation	dy+1/4(yd)x=32dx	$d y + (\frac{1}{4}) yd x = 32 d x$
72108	Solve the Differential Equation	dx-1/(y^2-6y+13)dy=0	$d x - \frac{1}{y^{2} - 6 y + 13} d y = 0$
72109	Solve the Differential Equation	(dy)/(dx)=y-xy^3e^(-2x)	$\frac{d y}{d x} = y - x y^{3} e^{- 2 x}$
72110	Solve the Differential Equation	xdy+3(yd)x=dx	$x d y + 3 yd x = d x$
72111	Solve the Differential Equation	y''''=4x-6	$y'' = 4 x - 6$
72112	Solve the Differential Equation	x(y+1)dx+y(x+1)dy=0	$x (y + 1) d x + y (x + 1) d y = 0$
72113	Solve the Differential Equation	t^2((dy)/(dt))+y^2=ty	$t^{2} (\frac{d y}{d t}) + y^{2} = t y$
72114	Solve the Differential Equation	(du)/(dt)=(5+t^4)/(ut^2+u^4t^2)	$\frac{d u}{d t} = \frac{5 + t^{4}}{u t^{2} + u^{4} t^{2}}$
72115	Solve the Differential Equation	(dy)/(dx)=4cos(2x)	$\frac{d y}{d x} = 4 \cos (2 x)$
72116	Solve the Differential Equation	y''''''''+2y''''+3y=0	$y'''' + 2 y'' + 3 y = 0$
72117	Solve the Differential Equation	2y(x^2-y+x)dx+(x^2-2y)dy=0	$2 y (x^{2} - y + x) d x + (x^{2} - 2 y) d y = 0$
72118	Solve the Differential Equation	(dy)/(dx)=3/(xy^2)	$\frac{d y}{d x} = \frac{3}{x y^{2}}$
72119	Solve the Differential Equation	(dy)/(dx)=12/x	$\frac{d y}{d x} = \frac{12}{x}$
72120	Solve the Differential Equation	(dy)/(dx)=( square root of x)/(e^y)	$\frac{d y}{d x} = \frac{\sqrt{x}}{e^{y}}$
72121	Solve the Differential Equation	(dy)/(dx)=-10x+12x^2	$\frac{d y}{d x} = - 10 x + 12 x^{2}$
72122	Solve the Differential Equation	4tx(dx)/(dt)=x^2+1	$4 t x \frac{d x}{d t} = x^{2} + 1$
72123	Solve the Differential Equation	(dy)/(dx)=(e^x)/y	$\frac{d y}{d x} = \frac{e^{x}}{y}$
72124	Solve the Differential Equation	(dy)/(dx)=3x-2	$\frac{d y}{d x} = 3 x - 2$
72125	Solve the Differential Equation	y^2(dy)/(dx)=x	$y^{2} \frac{d y}{d x} = x$
72126	Solve the Differential Equation	2x+2y(dy)/(dx)=0	$2 x + 2 y \frac{d y}{d x} = 0$
72127	Solve the Differential Equation	d/(dx)((dy)/(dx))=6x+3	$\frac{d}{d x} (\frac{d y}{d x}) = 6 x + 3$
72128	Solve the Differential Equation	xdy-(yd)x=0	$x d y - yd x = 0$
72129	Solve the Differential Equation	(dy)/(dx)-2y=0	$\frac{d y}{d x} - 2 y = 0$
72130	Solve the Differential Equation	(dy)/(dx)=(10e^x)/(e^y)	$\frac{d y}{d x} = \frac{10 e^{x}}{e^{y}}$
72131	Solve the Differential Equation	(dy)/(dx)=34x	$\frac{d y}{d x} = 34 x$
72132	Solve the Differential Equation	(dy)/(dx)=(-2x+y)^2-7	$\frac{d y}{d x} = {(- 2 x + y)}^{2} - 7$
72133	Solve the Differential Equation	(xy+y^2+x^2)dx-x^2dy=0	$(x y + y^{2} + x^{2}) d x - x^{2} d y = 0$
72134	Solve the Differential Equation	y''''=8 square root of y	$y'' = 8 \sqrt{y}$
72135	Solve the Differential Equation	2xy((dy)/(dx))=x^2+2y^2	$2 x y (\frac{d y}{d x}) = x^{2} + 2 y^{2}$
72136	Solve the Differential Equation	(dy)/(dx)-5y=-5/2xy^3	$\frac{d y}{d x} - 5 y = - \frac{5}{2} x y^{3}$
72137	Solve the Differential Equation	(4t^3y^3-2ty)dt+(3t^4y^2-t^2)dy=0	$(4 t^{3} y^{3} - 2 t y) d t + (3 t^{4} y^{2} - t^{2}) d y = 0$
72138	Solve the Differential Equation	(dy)/(dx)=5y^2cos(x)	$\frac{d y}{d x} = 5 y^{2} \cos (x)$
72139	Solve the Differential Equation	(2x+3y-5)dx+(3x-y-2)dy=0	$(2 x + 3 y - 5) d x + (3 x - y - 2) d y = 0$
72140	Solve the Differential Equation	y''''+y=2	$y'' + y = 2$
72141	Solve the Differential Equation	y''''''''=-y	$y'''' = - y$
72142	Solve the Differential Equation	y''''-2y=e^(2x)	$y'' - 2 y = e^{2 x}$
72143	Solve the Differential Equation	(dy)/(dx)=(y^2+x^2)/(2xy)	$\frac{d y}{d x} = \frac{y^{2} + x^{2}}{2 x y}$
72144	Solve the Differential Equation	(dy)/(dx)=-6x+12x^2	$\frac{d y}{d x} = - 6 x + 12 x^{2}$
72145	Solve the Differential Equation	y''''+2sin(2pix)=0	$y'' + 2 \sin (2 π x) = 0$
72146	Solve the Differential Equation	y^2dx-x^2dy=0	$y^{2} d x - x^{2} d y = 0$
72147	Solve the Differential Equation	f(x)=sin(sin(cos(x)))	$f (x) = \sin (\sin (\cos (x)))$
72148	Solve the Differential Equation	(du)/(dt)=(9+t^4)/(ut^2+u^4t^2)	$\frac{d u}{d t} = \frac{9 + t^{4}}{u t^{2} + u^{4} t^{2}}$
72149	Solve the Differential Equation	(dy)/(dx)=(xy+y^2+x^2)/(x^2)	$\frac{d y}{d x} = \frac{x y + y^{2} + x^{2}}{x^{2}}$
72150	Solve the Differential Equation	(dy)/(dx)=(x^2+y)/x	$\frac{d y}{d x} = \frac{x^{2} + y}{x}$
72151	Solve the Differential Equation	(dy)/(dx)=y-1	$\frac{d y}{d x} = y - 1$
72152	Solve the Differential Equation	(dy)/(dx)=(x^2+1)/(2-y)	$\frac{d y}{d x} = \frac{x^{2} + 1}{2 - y}$
72153	Solve the Differential Equation	(dy)/(dx)=x^4	$\frac{d y}{d x} = x^{4}$
72154	Solve the Differential Equation	y''''=e^(3x+2y)	$y'' = e^{3 x + 2 y}$
72155	Solve the Differential Equation	(3x^2y-6x)dx+(x^3+2y)dy=0	$(3 x^{2} y - 6 x) d x + (x^{3} + 2 y) d y = 0$
72156	Solve the Differential Equation	(dx)/(dy)=x/y	$\frac{d x}{d y} = \frac{x}{y}$
72157	Solve the Differential Equation	(dy)/(dx)=-8x+15x^2	$\frac{d y}{d x} = - 8 x + 15 x^{2}$
72158	Solve the Differential Equation	(dy)/(dx)=-(e^xy^2)/10	$\frac{d y}{d x} = - \frac{e^{x} y^{2}}{10}$
72159	Solve the Differential Equation	(x^2+9)dy=2x(yd)x	$(x^{2} + 9) d y = 2 x yd x$
72160	Solve the Differential Equation	(dy)/(dx)=(y^2+x square root of x^2+y^2)/(xy)	$\frac{d y}{d x} = \frac{y^{2} + x \sqrt{x^{2} + y^{2}}}{x y}$
72161	Solve the Differential Equation	2xy+(1+x^2)(dy)/(dx)=0 , y(0)=1	$2 x y + (1 + x^{2}) \frac{d y}{d x} = 0$ , $y (0) = 1$
72162	Solve the Differential Equation	(dy)/(dx)=12x^11y	$\frac{d y}{d x} = 12 x^{11} y$
72163	Solve the Differential Equation	2x^2-3(dy)/(dx)=5	$2 x^{2} - 3 \frac{d y}{d x} = 5$
72164	Solve the Differential Equation	(x^2+y^2)dx-x(yd)y=0	$(x^{2} + y^{2}) d x - x yd y = 0$
72165	Solve the Differential Equation	2xy(dy)/(dx)=4x^2+3y^2	$2 x y \frac{d y}{d x} = 4 x^{2} + 3 y^{2}$
72166	Solve the Differential Equation	(dM)/(dt)=a-kM	$\frac{d M}{d t} = a - k M$
72167	Solve the Differential Equation	yy''''+x=0	$y y'' + x = 0$
72168	Solve the Differential Equation	(2x^2+3y^2)dy+(3x^2+4xy)dx=0	$(2 x^{2} + 3 y^{2}) d y + (3 x^{2} + 4 x y) d x = 0$
72169	Solve the Differential Equation	y''''+xy=x^3	$y'' + x y = x^{3}$
72170	Solve the Differential Equation	(dy)/(dx)=9x^2-4x+5 ; where y(-1)=0	$\frac{d y}{d x} = 9 x^{2} - 4 x + 5$ ; where $y (- 1) = 0$
72171	Solve the Differential Equation	xy^2dy-(x^3+y^3)dx=0	$x y^{2} d y - (x^{3} + y^{3}) d x = 0$
72172	Solve the Differential Equation	(dy)/(dx)=-y^2	$\frac{d y}{d x} = - y^{2}$
72173	Solve the Differential Equation	y''''=3xy	$y'' = 3 x y$
72174	Solve the Differential Equation	(dr)/(ds)=0.75r	$\frac{d r}{d s} = 0.75 r$
72175	Solve the Differential Equation	y=f(x)	$y = f (x)$
72176	Solve the Differential Equation	(x^5+3y)dx-10dy=0	$(x^{5} + 3 y) d x - 10 d y = 0$
72177	Solve the Differential Equation	y''''=xy^3	$y'' = x y^{3}$
72178	Solve the Differential Equation	3xdy-(yd)x=9xdx	$3 x d y - yd x = 9 x d x$
72179	Solve the Differential Equation	(dy)/(dx)+4x^3=6x^2	$\frac{d y}{d x} + 4 x^{3} = 6 x^{2}$
72180	Solve the Differential Equation	(dy)/(dt)=ky(1-y)	$\frac{d y}{d t} = k y (1 - y)$
72181	Solve the Differential Equation	xy''''+y=x^2y^2	$x y'' + y = x^{2} y^{2}$
72182	Solve the Differential Equation	dy+ydx=2dx	$d y + yd x = 2 d x$
72183	Solve the Differential Equation	2xe^(2t)dt+(1+e^(2t))dx=0	$2 x e^{2 t} d t + (1 + e^{2 t}) d x = 0$
72184	Solve the Differential Equation	(dr)/(dtheta)=sin(pitheta)^4	$\frac{d r}{d θ} = \sin^{4} (π θ)$
72185	Solve the Differential Equation	(dP)/(dt)=5 square root of Pt	$\frac{d P}{d t} = 5 \sqrt{P t}$
72186	Solve the Differential Equation	(dy)/(x^2)=3y^2dx	$\frac{d y}{x^{2}} = 3 y^{2} d x$
72187	Solve the Differential Equation	(dy)/(dx)=x-1	$\frac{d y}{d x} = x - 1$
72188	Solve the Differential Equation	(x+y)dx+xdy=0	$(x + y) d x + x d y = 0$
72189	Solve the Differential Equation	(dy)/(dx)=y+e^x	$\frac{d y}{d x} = y + e^{x}$
72190	Solve the Differential Equation	y''''-y=2e^x	$y'' - y = 2 e^{x}$
72191	Solve the Differential Equation	y/xdx+(y^2+ natural log of \|x\|)dy=0	$\frac{y}{x} d x + (y^{2} + \ln (\| x \|)) d y = 0$
72192	Solve the Differential Equation	(dy)/(dx)=(-5x+y)^2-4	$\frac{d y}{d x} = {(- 5 x + y)}^{2} - 4$
72193	Solve the Differential Equation	(dy)/(dx)+1/xy=1/(xy^2)	$\frac{d y}{d x} + \frac{1}{x} y = \frac{1}{x y^{2}}$
72194	Solve the Differential Equation	(dy)/(dx)=10x	$\frac{d y}{d x} = 10 x$
72195	Verify the Differential Equation Solution	y=(x^3)/3 solve y''''=x^2	$y = \frac{x^{3}}{3}$ solve $y'' = x^{2}$
72196	Solve the Differential Equation	(y^2+xy)dx-x^2dy=0	$(y^{2} + x y) d x - x^{2} d y = 0$
72197	Solve the Differential Equation	cos(x)(dy)/(dx)+y=sin(x)	$\cos (x) \frac{d y}{d x} + y = \sin (x)$
72198	Solve the Differential Equation	(dy)/(dx)+y=y^2e^x	$\frac{d y}{d x} + y = y^{2} e^{x}$
72199	Solve the Differential Equation	y''''-4y''''+5y=0	$y'' - 4 y'' + 5 y = 0$
72200	Solve the Differential Equation	2x(3x+y-ye^(-x^2))dx+(x^2+3y^2+e^(-x^2))dy=0	$2 x (3 x + y - y e^{- x^{2}}) d x + (x^{2} + 3 y^{2} + e^{- x^{2}}) d y = 0$