(dy)/(dt)=(3t^2+4t+2)/(2(y-1))

Lösung

\frac{d y}{d t} = \frac{3 t ^{2} + 4 t + 2}{2 ( y - 1 )}

y = 1 + t^{3} + 2 t^{2} + 2 t + c_{1} + 1, y = 1 - t^{3} + 2 t^{2} + 2 t + c_{1} + 1

Schritte zur Lösung

\frac{d y}{d t} = \frac{3 t ^{2} + 4 t + 2}{2 ( y - 1 )}

Solve separable ODE:

y = 1 + t^{3} + 2 t^{2} + 2 t + c_{1} + 1, y = 1 - t^{3} + 2 t^{2} + 2 t + c_{1} + 1

y = 1 + t^{3} + 2 t^{2} + 2 t + c_{1} + 1, y = 1 - t^{3} + 2 t^{2} + 2 t + c_{1} + 1

2 y + 3 + (2 x - 4) y^{^{'}} = 0

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

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

y^{^{'}} + \frac{1}{x} y = y

x y^{3} + (1 - x) y^{^{'}} = 0