x^'=x-tx-t+1

Lösung

x^{^{'}} = x - t x - t + 1

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

Schritte zur Lösung

x^{'} (t) = x - t x - t + 1

Solve separable ODE:

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

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

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

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

\frac{d}{d x} (2 y ln (y)) = \frac{d x}{d x}

\frac{d y}{d x} = x^{2} y^{5}

\frac{d}{d θ} (ln (y (θ))) = \frac{θ - 3}{θ cos ( θ )}