What is the solution for (dy)/(dx)=xy^2e^x,y(0)=2 ?

The solution for (dy)/(dx)=xy^2e^x,y(0)=2 is y=-2/(2e^xx-2e^x+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=xy^2e^x,y(0)=2

\frac{d y}{d x} = x y^{2} e^{x}, y (0) = 2

y = - \frac{2}{2 e ^{x} x - 2 e ^{x} + 1}

Solution steps

\frac{d y}{d x} = x y^{2} e^{x}

Solve separable ODE:

y = - \frac{2}{2 e ^{x} x - 2 e ^{x} + 1}

y = - \frac{2}{2 e ^{x} x - 2 e ^{x} + 1}

\frac{d y}{d x} = \frac{x ^{2} - 1}{y ^{2}}, y (0) = 2

\frac{d x}{d y} = \frac{1 + x ^{2}}{y}

cos (y) \frac{d y}{d x} = \frac{- x sin ( y )}{1 + x ^{2}}

2 x^{^{'}} + x = 10

y y^{^{'}} = x e^{- y^{2}}

What is the solution for (dy)/(dx)=xy^2e^x,y(0)=2 ?
The solution for (dy)/(dx)=xy^2e^x,y(0)=2 is y=-2/(2e^xx-2e^x+1)