y^'-a^2ky+b^2=0

Lösung

y^{^{'}} - a^{2} k y + b^{2} = 0

y = \frac{e ^{t k a^{2} + c_{1} k a^{2}}}{k a ^{2}} + \frac{b ^{2}}{k a ^{2}}

Schritte zur Lösung

y^{'} (t) - a^{2} k y + b^{2} = 0

Solve separable ODE:

y = \frac{e ^{t k a^{2} + c_{1} k a^{2}}}{k a ^{2}} + \frac{b ^{2}}{k a ^{2}}

y = \frac{e ^{t k a^{2} + c_{1} k a^{2}}}{k a ^{2}} + \frac{b ^{2}}{k a ^{2}}

y^{^{'}} - 2 t y^{3} = 0

\frac{d y}{d t} = - k y

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

\frac{d y}{d t} = (2 + 3 t) y

\frac{d y}{d x} = - 7 y