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

The solution for (dy)/(dx)+x(y^2+y)=0 is y=(e^{c_{1}}(e^{(x^2)/2}+e^{c_{1}}))/(e^{x^2)-e^{2c_{1}}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)+x(y^2+y)=0

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

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

Solution steps

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

Solve separable ODE:

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

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

\int \frac{2 tan ( x )}{1 - tan ^{2} ( x )} d x

\frac{d}{d x} (tan (2 x + 1))

y = x^{3} + 6 x

4 + x^{6}

f (x) = 2 x 4 - x^{2}

What is the solution for (dy)/(dx)+x(y^2+y)=0 ?
The solution for (dy)/(dx)+x(y^2+y)=0 is y=(e^{c_{1}}(e^{(x^2)/2}+e^{c_{1}}))/(e^{x^2)-e^{2c_{1}}}