Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
72201	Solve the Differential Equation	(dy)/(dx)=x+2y	$\frac{d y}{d x} = x + 2 y$
72202	Solve the Differential Equation	(x+1)dy=(x+6)dx	$(x + 1) d y = (x + 6) d x$
72203	Solve the Differential Equation	xcos(ydx)^2+tan(ydy)=0	$x \cos^{2} (yd x) + \tan (yd y) = 0$
72204	Verify the Existence and Uniqueness of Solutions for the Differential Equation	(dy)/(dx) = square root of x-y , (1,2)	$\frac{d y}{d x} = \sqrt{x - y}$ , $(1, 2)$
72205	Solve the Differential Equation	y''''=e^x	$y'' = e^{x}$
72206	Solve the Differential Equation	(dy)/(dx)=-2+e^(2x+y-1)	$\frac{d y}{d x} = - 2 + e^{2 x + y - 1}$
72207	Solve the Differential Equation	(dy)/(dx)=-0.8y	$\frac{d y}{d x} = - 0.8 y$
72208	Solve the Differential Equation	(6x^2-y+3)dx+(3y^2-x-2)dy=0	$(6 x^{2} - y + 3) d x + (3 y^{2} - x - 2) d y = 0$
72209	Solve the Differential Equation	2x(yd)x+(x^2-1)dy=0	$2 x yd x + (x^{2} - 1) d y = 0$
72210	Solve the Differential Equation	square root of xdy = square root of ydx	$\sqrt{x} d y = \sqrt{y} d x$
72211	Solve the Differential Equation	(dy)/(dx)=-10x+15x^2	$\frac{d y}{d x} = - 10 x + 15 x^{2}$
72212	Solve the Differential Equation	(dy)/(dt)+2y=3	$\frac{d y}{d t} + 2 y = 3$
72213	Solve the Differential Equation	y(x+y+1)dx+x(x+3y+2)dy=0	$y (x + y + 1) d x + x (x + 3 y + 2) d y = 0$
72214	Solve the Differential Equation	(dy)/(dx) = square root of yx	$\frac{d y}{d x} = \sqrt{y x}$
72215	Solve the Differential Equation	e^(x^3)(3x^2y-x^2)dx+e^(x^3)dy=0	$e^{x^{3}} (3 x^{2} y - x^{2}) d x + e^{x^{3}} d y = 0$
72216	Solve the Differential Equation	xy''''+y=y^2 natural log of x	$x y'' + y = y^{2} \ln (x)$
72217	Solve the Differential Equation	(2x-y)dx-(x+4y)dy=0	$(2 x - y) d x - (x + 4 y) d y = 0$
72218	Solve the Differential Equation	(2x^3+3y)dx+(3x+y-1)dy=0	$(2 x^{3} + 3 y) d x + (3 x + y - 1) d y = 0$
72219	Solve the Differential Equation	y''''''''-4y''''+13y=0	$y'''' - 4 y'' + 13 y = 0$
72220	Solve the Differential Equation	x(dy)/(dx)-2y=3x^2+2x	$x \frac{d y}{d x} - 2 y = 3 x^{2} + 2 x$
72221	Solve the Differential Equation	y''''=y/(x^2)	$y'' = \frac{y}{x^{2}}$
72222	Solve the Differential Equation	(dy)/(dx)=8x^3y-8xy	$\frac{d y}{d x} = 8 x^{3} y - 8 x y$
72223	Solve the Differential Equation	y''''''''+3y''''=0	$y'''' + 3 y'' = 0$
72224	Solve the Differential Equation	(dy)/(dx)=-2x+12x^2	$\frac{d y}{d x} = - 2 x + 12 x^{2}$
72225	Solve the Differential Equation	(dy)/(dx)=sin(2x)	$\frac{d y}{d x} = \sin (2 x)$
72226	Solve the Differential Equation	(x+y-2)dx+(x-y+4)dy=0	$(x + y - 2) d x + (x - y + 4) d y = 0$
72227	Solve the Differential Equation	(dy)/(dx)-y/x=2+ square root of x	$\frac{d y}{d x} - \frac{y}{x} = 2 + \sqrt{x}$
72228	Solve the Differential Equation	(xe^(y/x)+y)dx-xdy=0	$(x e^{\frac{y}{x}} + y) d x - x d y = 0$
72229	Solve the Differential Equation	(dy)/(dx)=3+2y	$\frac{d y}{d x} = 3 + 2 y$
72230	Solve the Differential Equation	(dy)/(dx)=x+y+1	$\frac{d y}{d x} = x + y + 1$
72231	Solve the Differential Equation	(dy)/(dx)=xy+x^2	$\frac{d y}{d x} = x y + x^{2}$
72232	Solve the Differential Equation	(dy)/(dx)=12e^(x-y)	$\frac{d y}{d x} = 12 e^{x - y}$
72233	Solve the Differential Equation	(dy)/(dx)=2yx+yx^2	$\frac{d y}{d x} = 2 y x + y x^{2}$
72234	Solve the Differential Equation	y''''+2y=1	$y'' + 2 y = 1$
72235	Solve the Differential Equation	(dx)/(dt)=9/x	$\frac{d x}{d t} = \frac{9}{x}$
72236	Solve the Differential Equation	(dy)/(dx)=9e^(x-y)	$\frac{d y}{d x} = 9 e^{x - y}$
72237	Solve the Differential Equation	(dy)/(dx)=8e^(-4x)	$\frac{d y}{d x} = 8 e^{- 4 x}$
72238	Solve the Differential Equation	(du)/(dt)=(7+t^4)/(ut^2+u^4t^2)	$\frac{d u}{d t} = \frac{7 + t^{4}}{u t^{2} + u^{4} t^{2}}$
72239	Solve the Differential Equation	y''''+x^2y=x^2	$y'' + x^{2} y = x^{2}$
72240	Solve the Differential Equation	(dy)/(dx)=x(1+y)	$\frac{d y}{d x} = x (1 + y)$
72241	Solve the Differential Equation	(dy)/(dx)-4xy=0	$\frac{d y}{d x} - 4 x y = 0$
72242	Solve the Differential Equation	y''''=y(1-y)	$y'' = y (1 - y)$
72243	Solve the Differential Equation	f(x)=xcos(x)	$f (x) = x \cos (x)$
72244	Solve the Differential Equation	(y^2+7xy+16x^2)dx+x^2dy=0	$(y^{2} + 7 x y + 16 x^{2}) d x + x^{2} d y = 0$
72245	Solve the Differential Equation	(dy)/(dx)=( natural log of x)/(xy) , y(1)=2	$\frac{d y}{d x} = \frac{\ln (x)}{x y}$ , $y (1) = 2$
72246	Solve the Differential Equation	y''''=-y^2	$y'' = - y^{2}$
72247	Solve the Differential Equation	(dy)/(dx)+y/x=e^x	$\frac{d y}{d x} + \frac{y}{x} = e^{x}$
72248	Solve the Differential Equation	y''''-9y=0	$y'' - 9 y = 0$
72249	Solve the Differential Equation	2x^2(dy)/(dx)=x^2+y^2	$2 x^{2} \frac{d y}{d x} = x^{2} + y^{2}$
72250	Solve the Differential Equation	(dy)/(dx)=(2x+xy^2)/(4y+yx^2)	$\frac{d y}{d x} = \frac{2 x + x y^{2}}{4 y + y x^{2}}$
72251	Solve the Differential Equation	(2y^2t-2y^3)dt+(4y^3-6y^2t+2yt^2)dy=0	$(2 y^{2} t - 2 y^{3}) d t + (4 y^{3} - 6 y^{2} t + 2 y t^{2}) d y = 0$
72252	Solve the Differential Equation	(2x^2y+2x)((dy)/(dx))+2xy^2+2y=0	$(2 x^{2} y + 2 x) (\frac{d y}{d x}) + 2 x y^{2} + 2 y = 0$
72253	Solve the Differential Equation	(6x^2-7y^2)dx-14x(yd)y=0	$(6 x^{2} - 7 y^{2}) d x - 14 x yd y = 0$
72254	Solve the Differential Equation	y''''=y-xy^3e^(-2x)	$y'' = y - x y^{3} e^{- 2 x}$
72255	Solve the Differential Equation	y''''=(2y+x)/x	$y'' = \frac{2 y + x}{x}$
72256	Solve the Differential Equation	(dy)/(dx)=10x^9y	$\frac{d y}{d x} = 10 x^{9} y$
72257	Solve the Differential Equation	y''''=(x^2)/(y(1+x^3))	$y'' = \frac{x^{2}}{y (1 + x^{3})}$
72258	Solve the Differential Equation	(dy)/(dx)=y/x+2 square root of y/x	$\frac{d y}{d x} = \frac{y}{x} + 2 \sqrt{\frac{y}{x}}$
72259	Solve the Differential Equation	(dy)/(dx)=3 square root of xy	$\frac{d y}{d x} = 3 \sqrt{x y}$
72260	Solve the Differential Equation	8y(dy)/(dx)=3x^2	$8 y \frac{d y}{d x} = 3 x^{2}$
72261	Solve the Differential Equation	(dy)/(dt)=5	$\frac{d y}{d t} = 5$
72262	Solve the Differential Equation	((5y)/x-24x^2)dx+5dy=0	$(\frac{5 y}{x} - 24 x^{2}) d x + 5 d y = 0$
72263	Solve the Differential Equation	(dy)/(dx)+y/x=3/y	$\frac{d y}{d x} + \frac{y}{x} = \frac{3}{y}$
72264	Solve the Differential Equation	(dy)/(dx)=(y^2-x^2)/(2xy)	$\frac{d y}{d x} = \frac{y^{2} - x^{2}}{2 x y}$
72265	Solve the Differential Equation	(dN)/(dt)=kN	$\frac{d N}{d t} = k N$
72266	Solve the Differential Equation	3x(yd)x+(x^2+y^2)dy=0	$3 x yd x + (x^{2} + y^{2}) d y = 0$
72267	Solve the Differential Equation	(dy)/(dx)=(4x^3+3x^2+1)/(3y^2)	$\frac{d y}{d x} = \frac{4 x^{3} + 3 x^{2} + 1}{3 y^{2}}$
72268	Solve the Differential Equation	y''''''''-4y''''=0	$y'''' - 4 y'' = 0$
72269	Solve the Differential Equation	3(dy)/(dx)-15xy-5x=0	$3 \frac{d y}{d x} - 15 x y - 5 x = 0$
72270	Solve the Differential Equation	(dy)/(dx)=(y+1)/(x-1)	$\frac{d y}{d x} = \frac{y + 1}{x - 1}$
72271	Solve the Differential Equation	y''''=(x+1)e^(-x)y^2	$y'' = (x + 1) e^{- x} y^{2}$
72272	Solve the Differential Equation	y''''+y/x=3x	$y'' + \frac{y}{x} = 3 x$
72273	Solve the Differential Equation	(6x+3y)dx+(3x+9y)dy=0	$(6 x + 3 y) d x + (3 x + 9 y) d y = 0$
72274	Solve the Differential Equation	y''''+1/xy=0	$y'' + \frac{1}{x} y = 0$
72275	Solve the Differential Equation	(x-1)dx-(3x-2y-5)dy=0	$(x - 1) d x - (3 x - 2 y - 5) d y = 0$
72276	Solve the Differential Equation	y^2dx+(2xy-5x^3)dy=0	$y^{2} d x + (2 x y - 5 x^{3}) d y = 0$
72277	Solve the Differential Equation	e^xy''''-x=y''''	$e^{x} y'' - x = y''$
72278	Solve the Differential Equation	(dy)/(dx)-4y=0	$\frac{d y}{d x} - 4 y = 0$
72279	Solve the Differential Equation	(x^2-2y^2)dx+x(yd)y=0	$(x^{2} - 2 y^{2}) d x + x yd y = 0$
72280	Solve the Differential Equation	(2x^3-y^2-2y+3)dx+(x^2y+2x)dy=0	$(2 x^{3} - y^{2} - 2 y + 3) d x + (x^{2} y + 2 x) d y = 0$
72281	Solve the Differential Equation	xyy''''=x^2+1	$x y y'' = x^{2} + 1$
72282	Solve the Differential Equation	sin(x)sin(y)dx+cos(x)cos(y)dy=0	$\sin (x) \sin (y) d x + \cos (x) \cos (y) d y = 0$
72283	Solve the Differential Equation	(dr)/(dtheta)=(rtheta+r)/(rtheta+theta) , r(1)=e	$\frac{d r}{d θ} = \frac{r θ + r}{r θ + θ}$ , $r (1) = e$
72284	Solve the Differential Equation	(2xy-sec(x)^2)dx+(x^2+2)dy=0	$(2 x y - \sec^{2} (x)) d x + (x^{2} + 2) d y = 0$
72285	Solve the Differential Equation	(dy)/(dx)=15xy	$\frac{d y}{d x} = 15 x y$
72286	Solve the Differential Equation	(9x^2+y-1)dx-(4y-x)dy=0	$(9 x^{2} + y - 1) d x - (4 y - x) d y = 0$
72287	Solve the Differential Equation	2x(1+y^2)dx-y(1+2x^2)dy=0	$2 x (1 + y^{2}) d x - y (1 + 2 x^{2}) d y = 0$
72288	Solve the Differential Equation	(dy)/(dx)=3x^2+1	$\frac{d y}{d x} = 3 x^{2} + 1$
72289	Solve the Differential Equation	(dy)/(dx)+5xy=6x	$\frac{d y}{d x} + 5 x y = 6 x$
72290	Solve the Differential Equation	(du)/(dt)=(2t+sec(t)^2)/(2u) , u(0)=-6	$\frac{d u}{d t} = \frac{2 t + \sec^{2} (t)}{2 u}$ , $u (0) = - 6$
72291	Solve the Differential Equation	(dy)/(dx)=x^2-3	$\frac{d y}{d x} = x^{2} - 3$
72292	Solve the Differential Equation	x(dy)/(dx)=y+xy	$x \frac{d y}{d x} = y + x y$
72293	Solve the Differential Equation	f(x) = square root of x+3	$f (x) = \sqrt{x + 3}$
72294	Solve the Differential Equation	(dy)/(dx)=(3x^2+y^2)/(xy)	$\frac{d y}{d x} = \frac{3 x^{2} + y^{2}}{x y}$
72295	Solve the Differential Equation	y''''=y-y^2	$y'' = y - y^{2}$
72296	Solve the Differential Equation	x^2y''''+2xy-y^3=0	$x^{2} y'' + 2 x y - y^{3} = 0$
72297	Solve the Differential Equation	(dy)/(dx)=e^(2x+3y)	$\frac{d y}{d x} = e^{2 x + 3 y}$
72298	Solve the Differential Equation	(dy)/(dx)=(y^2-x^2)/(3xy)	$\frac{d y}{d x} = \frac{y^{2} - x^{2}}{3 x y}$
72299	Solve the Differential Equation	(dy)/(dx)=4x^3y-y , y(1)=-3	$\frac{d y}{d x} = 4 x^{3} y - y$ , $y (1) = - 3$
72300	Solve the Differential Equation	xyy''''+y^2-3x^2y^5=0	$x y y'' + y^{2} - 3 x^{2} y^{5} = 0$