xy^'-y^2-y=0

Lösung

x y^{^{'}} - y^{2} - y = 0

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

Schritte zur Lösung

x y^{'} (x) - y^{2} - y = 0

Solve separable ODE:

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

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

y + y^{^{'}} - 6 y = 0

f (x) = \frac{x ( 2 x - 1 )}{f ^{^{'}} ( x )}

y^{^{'}} + 2 x y = - 6 x

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

y - 6 y^{^{'}} + 13 y = 0, y (0) = e^{3} x cos (2 x)