y^'=xy-2x

Lösung

y^{^{'}} = x y - 2 x

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

Schritte zur Lösung

y^{'} (x) = x y - 2 x

Solve separable ODE:

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

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

y y^{^{'}} = x - y x, y (1) = 0

y^{^{'}} = y ln (y)

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

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

y^{^{'}} + y = - 2