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

Lösung

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

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{31 x}{2}) + c_{2} sin (\frac{31 x}{2})) + e^{\frac{3 x}{2}} cos (\frac{31 x}{2}) \cdot \int - \frac{2 31 sin ( \frac{31 x}{2} ) cosh ( 2 x )}{31 e ^{\frac{3 x}{2}}} d x + e^{\frac{3 x}{2}} sin (\frac{31 x}{2}) \cdot \int \frac{2 31 cos ( \frac{31 x}{2} ) cosh ( 2 x )}{31 e ^{\frac{3 x}{2}}} d x

Schritte zur Lösung

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

Solve linear ODE:

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{31 x}{2}) + c_{2} sin (\frac{31 x}{2})) + e^{\frac{3 x}{2}} cos (\frac{31 x}{2}) \cdot \int - \frac{2 31 sin ( \frac{31 x}{2} ) cosh ( 2 x )}{31 e ^{\frac{3 x}{2}}} d x + e^{\frac{3 x}{2}} sin (\frac{31 x}{2}) \cdot \int \frac{2 31 cos ( \frac{31 x}{2} ) cosh ( 2 x )}{31 e ^{\frac{3 x}{2}}} d x

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{31 x}{2}) + c_{2} sin (\frac{31 x}{2})) + e^{\frac{3 x}{2}} cos (\frac{31 x}{2}) \cdot \int - \frac{2 31 sin ( \frac{31 x}{2} ) cosh ( 2 x )}{31 e ^{\frac{3 x}{2}}} d x + e^{\frac{3 x}{2}} sin (\frac{31 x}{2}) \cdot \int \frac{2 31 cos ( \frac{31 x}{2} ) cosh ( 2 x )}{31 e ^{\frac{3 x}{2}}} d x

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

(d^{3} - 1) \cdot y = e^{x}

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

2 y^{^{''}} - 72 y = 0

y^{^{''}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 5