y^{''}-y^'-2y=x^2sin(2x)

Lösung

y^{^{''}} - y^{^{'}} - 2 y = x^{2} sin (2 x)

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{3 x ^{2} sin ( 2 x )}{20} + \frac{x ^{2} cos ( 2 x )}{20} - \frac{2 x sin ( 2 x )}{25} - \frac{19 x cos ( 2 x )}{100} + \frac{159}{2000} sin (2 x) - \frac{63}{2000} cos (2 x)

Schritte zur Lösung

y^{''} (x) - y^{'} (x) - 2 y = x^{2} sin (2 x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{3 x ^{2} sin ( 2 x )}{20} + \frac{x ^{2} cos ( 2 x )}{20} - \frac{2 x sin ( 2 x )}{25} - \frac{19 x cos ( 2 x )}{100} + \frac{159}{2000} sin (2 x) - \frac{63}{2000} cos (2 x)

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{3 x ^{2} sin ( 2 x )}{20} + \frac{x ^{2} cos ( 2 x )}{20} - \frac{2 x sin ( 2 x )}{25} - \frac{19 x cos ( 2 x )}{100} + \frac{159}{2000} sin (2 x) - \frac{63}{2000} cos (2 x)

y^{^{''}} + 16 y = g (t), y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} - 2 y^{^{'}} + y = 3 x^{\frac{3}{2}} e^{x}

2 y^{^{''}} + 5 y^{^{'}} + 2 y = x e^{- x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} - 3 y = 2 e^{x}

y^{^{''}} + 4 y^{^{'}} + 5 y = 2 e^{- 2 x} cos (x)