xyy^'=x^2e^{y/x}+y^2

Lösung

x y y^{^{'}} = x^{2} e^{\frac{y}{x}} + y^{2}

y = - W (\frac{ln ( x ) + c _{1}}{e}) x - x

Schritte zur Lösung

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

Solve using substitution:

y = - W (\frac{ln ( x ) + c _{1}}{e}) x - x

y = - W (\frac{ln ( x ) + c _{1}}{e}) x - x

(x + 3) (\frac{d y}{d x}) + y = ln (x)

\frac{\partial}{\partial y} (\frac{2 x}{y})

\frac{d y}{d x} - \frac{( 2 y )}{( 3 x )} + \frac{( x ^{2} + 2 )}{3} \cdot y^{4} = 0

x^{^{''}} + 3 x = 0

\int_{0}^{\frac{5}{2}} 25 - x^{2} d x