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

Lösung

y^{^{''}} + 4 y = \frac{e ^{2 x}}{x}

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

Schritte zur Lösung

y^{''} (x) + 4 y = \frac{e ^{2 x}}{x}

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} - 2 y = e^{3 t}

y^{^{''}} - y = 3 x^{2} - 1

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 e^{2 t} + 4 t^{2}

y^{^{'''}} - 8 y = e^{2 x}

y^{^{''}} - 4 y = x e^{x} + cos (2 x)