t^2y^{''}-2ty^'+2y=3t^2-t^3

Lösung

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

y = c_{1} t^{2} + c_{2} t + \frac{- t ^{3} + 6 t ^{2} ln ( t ) - 6 t ^{2}}{2}

Schritte zur Lösung

t^{2} y^{''} (t) - 2 t y^{'} (t) + 2 y = 3 t^{2} - t^{3}

Solve linear ODE:

y = c_{1} t^{2} + c_{2} t + \frac{- t ^{3} + 6 t ^{2} ln ( t ) - 6 t ^{2}}{2}

y = c_{1} t^{2} + c_{2} t + \frac{- t ^{3} + 6 t ^{2} ln ( t ) - 6 t ^{2}}{2}

f (t) = 6 t - 6 e^{t}

\int_{2}^{\infty} e^{- 7 p} d p

x \to - 2 lim (\frac{4}{x + 2})

\frac{d}{d x} (\frac{6 x}{x ^{2} + 4})

\int 99 - 2 x - x^{2} d x