What is the solution for (1+x^2)(dy)/(dx)=2xy+x^2+x^4 ?

The solution for (1+x^2)(dy)/(dx)=2xy+x^2+x^4 is y=x(1+x^2)-arctan(x)(1+x^2)+c_{1}(1+x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(1+x^2)(dy)/(dx)=2xy+x^2+x^4

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

y = x (1 + x^{2}) - arctan (x) (1 + x^{2}) + c_{1} (1 + x^{2})

Solution steps

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

Solve linear ODE:

y = x (1 + x^{2}) - arctan (x) (1 + x^{2}) + c_{1} (1 + x^{2})

y = x (1 + x^{2}) - arctan (x) (1 + x^{2}) + c_{1} (1 + x^{2})

\int \frac{1}{( 1 + e ^{x} )} d x

\frac{- 2}{( s + 1 ) ( s + 2 )}

x \to 0 lim (\frac{cos ( x ^{2} )}{x})

y^{^{''}} - 4 y^{^{'}} - 5 y = 50 t^{3}

\int \frac{e ^{- x} - e ^{2 x}}{2} d x

What is the solution for (1+x^2)(dy)/(dx)=2xy+x^2+x^4 ?
The solution for (1+x^2)(dy)/(dx)=2xy+x^2+x^4 is y=x(1+x^2)-arctan(x)(1+x^2)+c_{1}(1+x^2)