(d^2+4)y=sin^3(x)

Lösung

(d^{2} + 4) y = sin^{3} (x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{5} sin^{5} (x) cos (2 x) + sin (2 x) \cdot \int \frac{sin ^{3} ( x ) cos ( 2 x )}{2} d x

Schritte zur Lösung

(d^{2} + 4) y = sin^{3} (x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{5} sin^{5} (x) cos (2 x) + sin (2 x) \cdot \int \frac{sin ^{3} ( x ) cos ( 2 x )}{2} d x

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{5} sin^{5} (x) cos (2 x) + sin (2 x) \cdot \int \frac{sin ^{3} ( x ) cos ( 2 x )}{2} d x

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2} x

(d^{3} - 7 d - 6) y = e^{2} x (1 + x)

(d^{4} - 1) y = 7 x^{2}

(d^{3} - 5 d^{2} + 8 d - 4) y = e^{2} x

(d + 2 d^{2} + 1) y = cos (x)