(d^2+9)y=cos^4(x)

Lösung

(d^{2} + 9) y = cos^{4} (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + cos (3 x) \cdot \int - \frac{sin ( 3 x ) cos ^{4} ( x )}{3} d x + sin (3 x) \cdot \int \frac{cos ( 3 x ) cos ^{4} ( x )}{3} d x

Schritte zur Lösung

(d^{2} + 9) y = cos^{4} (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + cos (3 x) \cdot \int - \frac{sin ( 3 x ) cos ^{4} ( x )}{3} d x + sin (3 x) \cdot \int \frac{cos ( 3 x ) cos ^{4} ( x )}{3} d x

y = c_{1} cos (3 x) + c_{2} sin (3 x) + cos (3 x) \cdot \int - \frac{sin ( 3 x ) cos ^{4} ( x )}{3} d x + sin (3 x) \cdot \int \frac{cos ( 3 x ) cos ^{4} ( x )}{3} d x

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

y^{^{''}} + 8 y^{^{'}} + 15 y = 3 e^{- 3 t}

\frac{d ^{2} y}{d x ^{2}} + y = 3 cos (2 x)

y^{^{''}} + 2 y^{^{'}} = 3 + sin (t)

y^{^{''}} - 2 y + 10 y = e^{x} cos (3 x)