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

The solution for y^'= y/x+sqrt(1+(y/x)^2) is y=-1/(2e^{c_{1)}}+(e^{c_{1}}x^2)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'= y/x+sqrt(1+(y/x)^2)

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

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

Solution steps

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

Solve using substitution:

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

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

\int \frac{x ^{2} - 12}{x ^{3} + 4 x} d x

\frac{\partial}{\partial x} ((2 x y + 3) e^{- x y})

\frac{d}{d x} (\frac{( x ^{2} - 2 e ^{x} )}{x + 3 e ^{x}})

\int \frac{1}{x 3 x} d x

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

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