y^{''}+9y=t^2*e^{3t}+6

Lösung

y^{^{''}} + 9 y = t^{2} \cdot e^{3 t} + 6

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3 t} t ^{2}}{18} - \frac{e ^{3 t} t}{27} + \frac{1}{162} e^{3 t} + \frac{2}{3}

Schritte zur Lösung

y^{''} (t) + 9 y = t^{2} \cdot e^{3 t} + 6

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3 t} t ^{2}}{18} - \frac{e ^{3 t} t}{27} + \frac{1}{162} e^{3 t} + \frac{2}{3}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3 t} t ^{2}}{18} - \frac{e ^{3 t} t}{27} + \frac{1}{162} e^{3 t} + \frac{2}{3}

\int (\frac{6}{x}) d x

\frac{\partial}{\partial y} (4 x^{\frac{y}{z}})

\int_{0}^{4} x^{3} 7 - x^{2} d x

t an g e n t f (x) = x^{3} - \frac{2}{x ^{2}} + 2, (1, 3)

\frac{\partial}{\partial x} (x^{1})