y^{''}+9y=9cos^3(3x)

Lösung

y^{^{''}} + 9 y = 9 cos^{3} (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{4} cos^{5} (3 x) + sin (3 x) (cos^{3} (3 x) sin (3 x) + \frac{3}{8} (3 x - \frac{1}{4} sin (12 x)))

Schritte zur Lösung

y^{''} (x) + 9 y = 9 cos^{3} (3 x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{4} cos^{5} (3 x) + sin (3 x) (cos^{3} (3 x) sin (3 x) + \frac{3}{8} (3 x - \frac{1}{4} sin (12 x)))

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{4} cos^{5} (3 x) + sin (3 x) (cos^{3} (3 x) sin (3 x) + \frac{3}{8} (3 x - \frac{1}{4} sin (12 x)))

y^{^{''}} + 2 y^{^{'}} + 1 = t e^{t} sin (t)

y^{^{''''}} + 2 y^{^{''}} + y = 3 t + 10

y^{^{''}} - 5 y^{^{'}} + 6 y = \frac{e ^{2 x}}{1 + e ^{x}}

x^{^{''}} + 3 x^{^{'}} + 2 x = cos (t)

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