y^{''}+4y=sin^{22}(x)

Lösung

y^{^{''}} + 4 y = sin^{22} (x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{24} sin^{24} (x) cos (2 x) + sin (2 x) \cdot \int \frac{sin ^{22} ( x ) cos ( 2 x )}{2} d x

Schritte zur Lösung

y^{''} (x) + 4 y = sin^{22} (x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{24} sin^{24} (x) cos (2 x) + sin (2 x) \cdot \int \frac{sin ^{22} ( x ) cos ( 2 x )}{2} d x

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{24} sin^{24} (x) cos (2 x) + sin (2 x) \cdot \int \frac{sin ^{22} ( x ) cos ( 2 x )}{2} d x

y^{^{''}} - 3 y^{^{'}} = 2 - 6 x

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 1 + x e^{x}

6 y^{^{''}} + 4 y^{^{'}} - y = 25

10000 x^{^{''}} + 1000 x^{^{'}} + 22 x - 60000 = 0

y^{^{''}} + 3 y^{^{'}} + 6 \cdot x = 0