y^{''}+3y=-4x^2e^{3x}

Lösung

y^{^{''}} + 3 y = - 4 x^{2} e^{3 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{e ^{3 x} x ^{2}}{3} + \frac{e ^{3 x} x}{3} - \frac{1}{9} e^{3 x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{e ^{3 x} x ^{2}}{3} + \frac{e ^{3 x} x}{3} - \frac{1}{9} e^{3 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{e ^{3 x} x ^{2}}{3} + \frac{e ^{3 x} x}{3} - \frac{1}{9} e^{3 x}

y^{^{''}} + 9 y = 27 x^{3}

\frac{1}{4} y^{^{''}} + 4 y = tan (4 t) - \frac{1}{2} e^{2 t}

y^{^{''''}} + 2 y^{^{''}} + y = 11 + cos (3 t)

y^{^{''}} + 4 y = sin (3 t), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e x - 6