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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 40 y^{^{'}} + 400 y = 100 sin (10 t)

y^{^{''}} + 7 y = x

y^{^{''}} - y^{^{'}} - 6 y = 14 cos (3 x)

y^{^{''}} + 4000 y^{^{'}} + 4000000 y = 36

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 49 y = 4 e^{5 x}