What is the solution for (x^2y^3-1/(1+9x^2))((dx)/(dy))+x^3y^2=0 ?

The solution for (x^2y^3-1/(1+9x^2))((dx)/(dy))+x^3y^2=0 is y=(\sqrt[3]{arctan(3x)+c_{1}})/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x^2y^3-1/(1+9x^2))((dx)/(dy))+x^3y^2=0

(x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) (\frac{d x}{d y}) + x^{3} y^{2} = 0

y = \frac{3 arctan ( 3 x ) + c _{1}}{x}

Solution steps

(x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) (\frac{d}{d y} (x)) + x^{3} y^{2} = 0

Solve using substitution:

y = \frac{3 arctan ( 3 x ) + c _{1}}{x}

y = \frac{3 arctan ( 3 x ) + c _{1}}{x}

\int x^{2} 1 + x^{2} d x

\frac{\partial}{\partial x} (x^{2} sin (3 t))

arcsin (e^{2 x})

\int ln (sin (x)) cos^{3} (x) d x

t^{2} \frac{d y}{d t} + y = 0, y (5) = - 1, t > 0

What is the solution for (x^2y^3-1/(1+9x^2))((dx)/(dy))+x^3y^2=0 ?
The solution for (x^2y^3-1/(1+9x^2))((dx)/(dy))+x^3y^2=0 is y=(\sqrt[3]{arctan(3x)+c_{1}})/x