4y^{''}+36y=csc(x)

Lösung

4 y^{^{''}} + 36 y = csc (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + cos (3 x) \cdot \int - \frac{3 - 4 sin ^{2} ( x )}{12} d x + sin (3 x) \cdot \int \frac{csc ( x ) cos ( 3 x )}{12} d x

Schritte zur Lösung

4 y^{''} (x) + 36 y = csc (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + cos (3 x) \cdot \int - \frac{3 - 4 sin ^{2} ( x )}{12} d x + sin (3 x) \cdot \int \frac{csc ( x ) cos ( 3 x )}{12} d x

y = c_{1} cos (3 x) + c_{2} sin (3 x) + cos (3 x) \cdot \int - \frac{3 - 4 sin ^{2} ( x )}{12} d x + sin (3 x) \cdot \int \frac{csc ( x ) cos ( 3 x )}{12} d x

y^{^{''}} - 2 y^{^{'}} + y = x e^{x} + 4, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} - 6 y = u^{2} (t), y (0) = 0

y^{^{''}} + 16 y = e^{5 t}

y^{^{''}} + 256 y = 16 cos (3 x)

D (x) = - 6 (2940) + 4200