y^{''}+4y=(x^2-3)sin(2x)

Lösung

y^{^{''}} + 4 y = (x^{2} - 3) sin (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{3} cos ( 2 x )}{12} + \frac{x ^{2} sin ( 2 x )}{16} + \frac{25 x cos ( 2 x )}{32}

Schritte zur Lösung

y^{''} (x) + 4 y = (x^{2} - 3) sin (2 x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{3} cos ( 2 x )}{12} + \frac{x ^{2} sin ( 2 x )}{16} + \frac{25 x cos ( 2 x )}{32}

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{3} cos ( 2 x )}{12} + \frac{x ^{2} sin ( 2 x )}{16} + \frac{25 x cos ( 2 x )}{32}

y^{^{''}} - 5 y^{^{'}} - 6 y = 2 cos (3 x) + 4 e^{2 x}

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

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

y^{^{''}} + y^{^{'}} = sec (x) csc (x)

x^{^{''}} + x = cos (t)