y^'+5xy= x/2-xy

Lösung

y^{^{'}} + 5 x y = \frac{x}{2} - x y

y = \frac{e ^{- 3 x^{2} + c_{1}}}{12} + \frac{1}{12}

Schritte zur Lösung

y^{'} (x) + 5 x y = \frac{x}{2} - x y

Solve separable ODE:

y = \frac{e ^{- 3 x^{2} + c_{1}}}{12} + \frac{1}{12}

y = \frac{e ^{- 3 x^{2} + c_{1}}}{12} + \frac{1}{12}

\frac{d y}{d t} = 0.4 y

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

(5 + x) y^{^{'}} = 2 y

(1 - y^{2}) d x = - (x y - y) d y

e^{- y} + e^{- y} y^{^{'}} = 1