What is the solution for (dy)/(dx)=((2x)y)/(1+x^2) ?

The solution for (dy)/(dx)=((2x)y)/(1+x^2) is y=e^{c_{1}}+e^{c_{1}}x^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=((2x)y)/(1+x^2)

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

y = e^{c_{1}} + e^{c_{1}} x^{2}

Solution steps

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

Solve separable ODE:

y = e^{c_{1}} + e^{c_{1}} x^{2}

y = e^{c_{1}} + e^{c_{1}} x^{2}

\frac{d y}{d x} = \frac{5 x ^{4}}{3 y ^{2} e ^{y^{3}}}

u^{^{'}} = 6 e^{7 x - H (x)}

\frac{d y}{d x} = 9.8 y

y^{^{'}} = - 3 y + 2

x^{2} \frac{d y}{d x} = y (4 x + 5)

What is the solution for (dy)/(dx)=((2x)y)/(1+x^2) ?
The solution for (dy)/(dx)=((2x)y)/(1+x^2) is y=e^{c_{1}}+e^{c_{1}}x^2