y^{''}+25y=cos^5(x)

Lösung

y^{^{''}} + 25 y = cos^{5} (x)

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

Schritte zur Lösung

y^{''} (x) + 25 y = cos^{5} (x)

Solve linear ODE:

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

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

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = 30 e^{- x}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3} x

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

f^{^{''}} (x) + 9 f (x) = 1

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