(d^2y)/(dx^2)+2(dy)/(dx)-15y=7+4x

Lösung

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = 7 + 4 x

y = c_{1} e^{3 x} + c_{2} e^{- 5 x} - \frac{4 x}{15} - \frac{113}{225}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = 7 + 4 x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 5 x} - \frac{4 x}{15} - \frac{113}{225}

y = c_{1} e^{3 x} + c_{2} e^{- 5 x} - \frac{4 x}{15} - \frac{113}{225}

y^{^{''}} + 4 y = - 5 sin (2 t) + 2 cos (2 t)

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} = 2 e^{2 x}

\frac{d ^{2} y}{d t ^{2}} + 8 \frac{d y}{d t} + 15 y = 3

y^{^{''}} - 6 y^{^{'}} - 27 y = - 57 t + 54 t^{2}

y^{^{''}} + 15 y^{^{'}} + 56 y = 112 x^{2} + 60 x + 4 + 72 e^{x}