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

The solution for x(dy)/(dx)=y+sqrt(x^2+y^2),x>0 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 >

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

x \frac{d y}{d x} = y + x^{2} + y^{2}, x > 0

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

Solution steps

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

\int_{0}^{2} (4 - x)^{2} d x

\frac{- 2 x - y}{x + 3 y ^{2}}

\frac{d y}{d x} = \frac{( x - 3 )}{( y - 3 )}

\int (x + 4) (x - 2) d x

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