y^{''}+16y=12cos(4x)+18sin(4x)

Lösung

y^{^{''}} + 16 y = 12 cos (4 x) + 18 sin (4 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{3 x sin ( 4 x )}{2} - \frac{9 x cos ( 4 x )}{4}

Schritte zur Lösung

y^{''} (x) + 16 y = 12 cos (4 x) + 18 sin (4 x)

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{3 x sin ( 4 x )}{2} - \frac{9 x cos ( 4 x )}{4}

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{3 x sin ( 4 x )}{2} - \frac{9 x cos ( 4 x )}{4}

l in e a r - \frac{1}{4} y^{^{''}} + y^{^{'}} + y = x^{2} - 2 x

y^{^{''}} - 10 y^{^{'}} + 25 y = \frac{e ^{5 x}}{4 + x ^{2}}

y^{^{''}} + 4 y = x^{2} + sin (2 x)

\frac{d ^{2} y}{d x ^{2}} - y = sin (x) + e^{- 5 x}

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 x e^{3 x}