2y^{''}+50y=2cos(5x)cos(5x)

Lösung

2 y^{^{''}} + 50 y = 2 cos (5 x) cos (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{cos ^{4} ( 5 x ) + sin ( 5 x ) ( 3 sin ( 5 x ) - sin ^{3} ( 5 x ) )}{75}

Schritte zur Lösung

2 y^{''} (x) + 50 y = 2 cos (5 x) cos (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{cos ^{4} ( 5 x ) + sin ( 5 x ) ( 3 sin ( 5 x ) - sin ^{3} ( 5 x ) )}{75}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{cos ^{4} ( 5 x ) + sin ( 5 x ) ( 3 sin ( 5 x ) - sin ^{3} ( 5 x ) )}{75}

\frac{d ^{2} y}{d t ^{2}} + y = t^{2}

y^{^{''}} + 2 y^{^{'}} + 2 y = sec (x) e^{- x}

y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{e ^{(- 2 x)}}{x ^{3}}

y + 2 \frac{d ^{2} y}{d x ^{2}} = 1

y^{^{''}} - 5 y = 3 sin (2 \cdot π \cdot x)