3(d^2y)/(dx^2)-6(dy)/(dx)+30y=15sin(x)

Lösung

3 \frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 30 y = 15 sin (x)

y = e^{x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{9}{17} sin (x) + \frac{2}{17} cos (x)

Schritte zur Lösung

3 \frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 30 y = 15 sin (x)

Solve linear ODE:

y = e^{x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{9}{17} sin (x) + \frac{2}{17} cos (x)

y = e^{x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{9}{17} sin (x) + \frac{2}{17} cos (x)

y^{^{''}} - y^{^{'}} = 3 x

y^{^{''}} - y^{^{'}} + 9 y = 3 sin (3 x)

y^{^{''}} + y^{^{'}} = 4

y^{^{''}} + y^{^{'}} = e^{- x}

y^{^{''}} - 3 y^{^{'}} - 4 y = 4 x^{2}