(dx)/(dt)=(1+t)(1+x)

Lösung

\frac{d x}{d t} = (1 + t) (1 + x)

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

Schritte zur Lösung

\frac{d x}{d t} = (1 + t) (1 + x)

Solve separable ODE:

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

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

y^{^{'}} = 3 y, y (0) = 5

y^{^{'}} = 3 y, y (0) = 3

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

y^{^{'}} + y \frac{1 + 6 t ^{2}}{2 t + 3 t ^{3}} = 0

\frac{d y}{d t} + 2 y = 7