Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
74201	Solve the Differential Equation	e^(-y)cos(x)+(dy)/(dx)sin(x)^2=0	$e^{- y} \cos (x) + \frac{d y}{d x} \sin^{2} (x) = 0$
74202	Solve the Differential Equation	4(yd)x+xdy=0	$4 yd x + x d y = 0$
74203	Solve the Differential Equation	x^2(yd)x-(x^3+y^3)dy=0	$x^{2} yd x - (x^{3} + y^{3}) d y = 0$
74204	Solve the Differential Equation	(dy)/(dx)=2 square root of xy	$\frac{d y}{d x} = 2 \sqrt{x y}$
74205	Solve the Differential Equation	f(x) = square root of x+4	$f (x) = \sqrt{x + 4}$
74206	Solve the Differential Equation	yy''''=-x	$y y'' = - x$
74207	Solve the Differential Equation	(dy)/(dx)+3y=e^(2x)	$\frac{d y}{d x} + 3 y = e^{2 x}$
74208	Solve the Differential Equation	y''''=y^2-1	$y'' = y^{2} - 1$
74209	Solve the Differential Equation	(dy)/(dt)=-1/50(y-25)	$\frac{d y}{d t} = - \frac{1}{50} (y - 25)$
74210	Solve the Differential Equation	x(dy)/(dx)+2y=xy^2	$x \frac{d y}{d x} + 2 y = x y^{2}$
74211	Solve the Differential Equation	(dy)/(dx)=7/((4+x)^2) , y(0)=4	$\frac{d y}{d x} = \frac{7}{{(4 + x)}^{2}}$ , $y (0) = 4$
74212	Solve the Differential Equation	(dy)/(dt)=-2ty+4e^(-t^2)	$\frac{d y}{d t} = - 2 t y + 4 e^{- t^{2}}$
74213	Solve the Differential Equation	y(yy''''-1)=x	$y (y y'' - 1) = x$
74214	Solve the Differential Equation	2xy(dy)/(dx)+y^2-2x=0	$2 x y \frac{d y}{d x} + y^{2} - 2 x = 0$
74215	Solve the Differential Equation	9y(dy)/(dx)+4x=0	$9 y \frac{d y}{d x} + 4 x = 0$
74216	Solve the Differential Equation	y''''=y/x-1	$y'' = \frac{y}{x} - 1$
74217	Solve the Differential Equation	x(dy)/(dx)-5y=x^7	$x \frac{d y}{d x} - 5 y = x^{7}$
74218	Solve the Differential Equation	y''''+(1/x)y=x square root of y	$y'' + (\frac{1}{x}) y = x \sqrt{y}$
74219	Solve the Differential Equation	(dy)/(dx)=( square root of 4-x^2)/(2x)	$\frac{d y}{d x} = \frac{\sqrt{4 - x^{2}}}{2 x}$
74220	Solve the Differential Equation	(ds)/(dt)=cos(t)-sin(t) , s(pi/2)=9	$\frac{d s}{d t} = \cos (t) - \sin (t)$ , $s (\frac{π}{2}) = 9$
74221	Solve the Differential Equation	(xy-x)dx+(xy+x-y-1)dy=0	$(x y - x) d x + (x y + x - y - 1) d y = 0$
74222	Solve the Differential Equation	y^-1dy+ye^(cos(x))sin(xdx)=0	$y^{- 1} d y + y e^{\cos (x)} \sin (x d x) = 0$
74223	Solve the Differential Equation	y''''-4y''''=0	$y'' - 4 y'' = 0$
74224	Solve the Differential Equation	(d^2y)/(dx^2)+(dy)/(dx)+y=0	$\frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} + y = 0$
74225	Solve the Differential Equation	(dy)/(dx)+xy=0	$\frac{d y}{d x} + x y = 0$
74226	Solve the Differential Equation	x(dy)/(dx)+xy=1-y	$x \frac{d y}{d x} + x y = 1 - y$
74227	Solve the Differential Equation	(dy)/(dx)=(11x^2)/( square root of 8+x^3)	$\frac{d y}{d x} = \frac{11 x^{2}}{\sqrt{8 + x^{3}}}$
74228	Solve the Differential Equation	(x^2-yx^2)dy+(y^2+xy^2)dx=0	$(x^{2} - y x^{2}) d y + (y^{2} + x y^{2}) d x = 0$
74229	Solve the Differential Equation	y''''=-(sin(x))(cos(y)^2)	$y'' = - (\sin (x)) (\cos^{2} (y))$
74230	Solve the Differential Equation	h(theta)=theta^2sin(theta)	$h (θ) = θ^{2} \sin (θ)$
74231	Solve the Differential Equation	y''''''''+y=cos(x)^2	$y'''' + y = \cos^{2} (x)$
74232	Solve the Differential Equation	(x^2+y^2)dx=2x(yd)y	$(x^{2} + y^{2}) d x = 2 x yd y$
74233	Solve the Differential Equation	y''''=x^2y^3	$y'' = x^{2} y^{3}$
74234	Solve the Differential Equation	f(x) = square root of x+8	$f (x) = \sqrt{x + 8}$
74235	Solve the Differential Equation	(dy)/(dx)=4x^3-9x^2+5x	$\frac{d y}{d x} = 4 x^{3} - 9 x^{2} + 5 x$
74236	Solve the Differential Equation	(ds)/(dt)=12t(3t^2-1)^3 , s(1)=7	$\frac{d s}{d t} = 12 t {(3 t^{2} - 1)}^{3}$ , $s (1) = 7$
74237	Solve the Differential Equation	1/ydx-x/(y^2)dy=0	$\frac{1}{y} d x - \frac{x}{y^{2}} d y = 0$
74238	Solve the Differential Equation	(ds)/(dt)=36t(9t^2-7)^3 , s(1)=10	$\frac{d s}{d t} = 36 t {(9 t^{2} - 7)}^{3}$ , $s (1) = 10$
74239	Solve the Differential Equation	(y^2)/(x^2)-y/x+y''''=0	$\frac{y^{2}}{x^{2}} - \frac{y}{x} + y'' = 0$
74240	Solve the Differential Equation	2tds+s(2+s^2t)dt=0	$2 t d s + s (2 + s^{2} t) d t = 0$
74241	Solve the Differential Equation	(dy)/(dx)=(e^x+5)^2	$\frac{d y}{d x} = {(e^{x} + 5)}^{2}$
74242	Solve the Differential Equation	(dy)/(dx)-(3y)/x=2	$\frac{d y}{d x} - \frac{3 y}{x} = 2$
74243	Solve the Differential Equation	(x+2)dx-xdy=0	$(x + 2) d x - x d y = 0$
74244	Solve the Differential Equation	xdy-(y+1)dx=0	$x d y - (y + 1) d x = 0$
74245	Solve the Differential Equation	(2x^3-xy^2-2y+3)dx+(x^2y+2x)dy=0 ?	$(2 x^{3} - x y^{2} - 2 y + 3) d x + (x^{2} y + 2 x) d y = 0$ ?
74246	Solve the Differential Equation	(dy)/(dx)=x+5*x+xy	$\frac{d y}{d x} = x + 5 \cdot x + x y$
74247	Solve the Differential Equation	(dy)/(dx)=((1+3y)^2)/(e^(2x))	$\frac{d y}{d x} = \frac{{(1 + 3 y)}^{2}}{e^{2 x}}$
74248	Solve the Differential Equation	x(yd)x+(2x^2+3y^2-20)dy=0	$x yd x + (2 x^{2} + 3 y^{2} - 20) d y = 0$
74249	Solve the Differential Equation	y^4+y''''''''''''+y''''''''=0	$y^{4} + y'''''' + y'''' = 0$
74250	Solve the Differential Equation	ydx-2(x+y)dy=0	$yd x - 2 (x + y) d y = 0$
74251	Solve the Differential Equation	sin(x)dy+y^2cos(x)dx=0	$\sin (x) d y + y^{2} \cos (x) d x = 0$
74252	Solve the Differential Equation	(dr)/(dtheta)=picos(pitheta) , r(2)=3	$\frac{d r}{d θ} = π \cos (π θ)$ , $r (2) = 3$
74253	Solve the Differential Equation	y(x^3-y^5)dx-x(x^3+y^5)dy=0	$y (x^{3} - y^{5}) d x - x (x^{3} + y^{5}) d y = 0$
74254	Solve the Differential Equation	(ds)/(dt)=36t(9t^2-7)^3 , s(1)=2	$\frac{d s}{d t} = 36 t {(9 t^{2} - 7)}^{3}$ , $s (1) = 2$
74255	Solve the Differential Equation	(dy)/(dx)=2x square root of 1-y^2	$\frac{d y}{d x} = 2 x \sqrt{1 - y^{2}}$
74256	Solve the Differential Equation	(2x+y)dx-xdy=0	$(2 x + y) d x - x d y = 0$
74257	Solve the Differential Equation	y''''''''+y''''=8t	$y'''' + y'' = 8 t$
74258	Solve the Differential Equation	(yy'''')/x+e^y=0	$\frac{y y''}{x} + e^{y} = 0$
74259	Solve the Differential Equation	(dr)/(dtheta)=pisin(pitheta) , r(2)=3	$\frac{d r}{d θ} = π \sin (π θ)$ , $r (2) = 3$
74260	Solve the Differential Equation	(dy)/(dx)=e^x+sec(x)	$\frac{d y}{d x} = e^{x} + \sec (x)$
74261	Solve the Differential Equation	(x+y)dy+(y)dx=0	$(x + y) d y + (y) d x = 0$
74262	Solve the Differential Equation	x(1-y)(dy)/(dx)+(1-x)y=0	$x (1 - y) \frac{d y}{d x} + (1 - x) y = 0$
74263	Solve the Differential Equation	(dx)/(dy)=xye^(y^2)	$\frac{d x}{d y} = x y e^{y^{2}}$
74264	Solve the Differential Equation	(dy)/(dx)-1/xy=1	$\frac{d y}{d x} - \frac{1}{x} y = 1$
74265	Solve the Differential Equation	(dy)/(dx)=5x^(4/5)	$\frac{d y}{d x} = 5 x^{\frac{4}{5}}$
74266	Solve the Differential Equation	(dy)/(dx)=-(4x)/(3y)	$\frac{d y}{d x} = - \frac{4 x}{3 y}$
74267	Solve the Differential Equation	y''''+2xy=4x	$y'' + 2 x y = 4 x$
74268	Solve the Differential Equation	(1+t^2)(dy)/(dt)=1+y^2	$(1 + t^{2}) \frac{d y}{d t} = 1 + y^{2}$
74269	Solve the Differential Equation	(dy)/(dx)=e^(7x-7y)	$\frac{d y}{d x} = e^{7 x - 7 y}$
74270	Solve the Differential Equation	1/2y''''-y=0	$\frac{1}{2} y'' - y = 0$
74271	Solve the Differential Equation	y''''=6x	$y'' = 6 x$
74272	Solve the Differential Equation	(dy)/(dx)(1/x)-(2y)/(x^2)=xcos(x)	$\frac{d y}{d x} (\frac{1}{x}) - \frac{2 y}{x^{2}} = x \cos (x)$
74273	Solve the Differential Equation	xy^2y''''=x+6	$x y^{2} y'' = x + 6$
74274	Solve the Differential Equation	(dy)/(dx)=(y( natural log of y- natural log of x+1))/x	$\frac{d y}{d x} = \frac{y (\ln (y) - \ln (x) + 1)}{x}$
74275	Solve the Differential Equation	(x^2-1)(dy)/(dx)+2xy=x	$(x^{2} - 1) \frac{d y}{d x} + 2 x y = x$
74276	Solve the Differential Equation	f(x)=e^(7x)	$f (x) = e^{7 x}$
74277	Solve the Differential Equation	2(dy)/(dx)-14xy-7x=0	$2 \frac{d y}{d x} - 14 x y - 7 x = 0$
74278	Solve the Differential Equation	(dy)/(dx)=(4x^3)/(9e^y)	$\frac{d y}{d x} = \frac{4 x^{3}}{9 e^{y}}$
74279	Solve the Differential Equation	(tan(x)-sin(x)sin(y))dx+cos(x)cos(y)dy=0	$(\tan (x) - \sin (x) \sin (y)) d x + \cos (x) \cos (y) d y = 0$
74280	Solve the Differential Equation	xyy''''+4x^2+y^2=0	$x y y'' + 4 x^{2} + y^{2} = 0$
74281	Solve the Differential Equation	y''''+4/(x^2-1)y=0	$y'' + \frac{4}{x^{2} - 1} y = 0$
74282	Solve the Differential Equation	2xy''''+y=2 square root of x	$2 x y'' + y = 2 \sqrt{x}$
74283	Solve the Differential Equation	y''''+4y''''+8y=0	$y'' + 4 y'' + 8 y = 0$
74284	Solve the Differential Equation	(dy)/(dx)=(xy-y^2)/(x^2)	$\frac{d y}{d x} = \frac{x y - y^{2}}{x^{2}}$
74285	Solve the Differential Equation	(dA)/(dt)=-6A	$\frac{d A}{d t} = - 6 A$
74286	Solve the Differential Equation	(dy)/(dt)=5 square root of t , y(1)=4	$\frac{d y}{d t} = 5 \sqrt{t}$ , $y (1) = 4$
74287	Solve the Differential Equation	(dy)/(dx)=-(x-2)/(y+1)	$\frac{d y}{d x} = - \frac{x - 2}{y + 1}$
74288	Solve the Differential Equation	y''''=9x^2	$y'' = 9 x^{2}$
74289	Solve the Differential Equation	8x^3(yd)x+(2y^4-9x^4)dy=0	$8 x^{3} yd x + (2 y^{4} - 9 x^{4}) d y = 0$
74290	Solve the Differential Equation	(dy)/(dx) = square root of x+y-1	$\frac{d y}{d x} = \sqrt{x + y} - 1$
74291	Solve the Differential Equation	(dy)/(dx)=4x^3+2x	$\frac{d y}{d x} = 4 x^{3} + 2 x$
74292	Solve the Differential Equation	4x+2y(dy)/(dx)=0	$4 x + 2 y \frac{d y}{d x} = 0$
74293	Solve the Differential Equation	xtan(x)dx-ycos(x)dy=0	$x \tan (x) d x - y \cos (x) d y = 0$
74294	Solve the Differential Equation	y''''''''-2y''''+y=e^x	$y'''' - 2 y'' + y = e^{x}$
74295	Solve the Differential Equation	(dy)/(dx)=(4x^2)/( square root of 3+x^3)	$\frac{d y}{d x} = \frac{4 x^{2}}{\sqrt{3 + x^{3}}}$
74296	Solve the Differential Equation	y''''=x+y^2	$y'' = x + y^{2}$
74297	Solve the Differential Equation	6y(dy)/(dx)=7x^2	$6 y \frac{d y}{d x} = 7 x^{2}$
74298	Solve the Differential Equation	(dy)/(dt)=-1/50(y-23)	$\frac{d y}{d t} = - \frac{1}{50} (y - 23)$
74299	Verify the Differential Equation Solution	Solve x(dy)/(dx)=y^2+1 and find the particular solution when y(1)=1	Solve $x \frac{d y}{d x} = y^{2} + 1$ and find the particular solution when $y (1) = 1$
74300	Solve the Differential Equation	2y''''=y	$2 y'' = y$