(y^')/t =3y^2+2y+1

Lösung

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

y = \frac{2 tan ( \frac{t ^{2} + c _{1}}{2} )}{3} - \frac{1}{3}

Schritte zur Lösung

\frac{y ^{'} ( t )}{t} = 3 y^{2} + 2 y + 1

Solve separable ODE:

y = \frac{2 tan ( \frac{t ^{2} + c _{1}}{2} )}{3} - \frac{1}{3}

y = \frac{2 tan ( \frac{t ^{2} + c _{1}}{2} )}{3} - \frac{1}{3}

\frac{d v}{d x} = - 475000 - 5 v^{2}

y^{^{'}} - 9 y = 0

5 y^{4} \frac{d y}{d x} = 2 x

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

\frac{d y}{d x} = a - b \cdot y