y^{''}+4y=8x^2+7x

Lösung

y^{^{''}} + 4 y = 8 x^{2} + 7 x

y = c_{1} cos (2 x) + c_{2} sin (2 x) + 2 x^{2} + \frac{7 x}{4} - 1

Schritte zur Lösung

y^{''} (x) + 4 y = 8 x^{2} + 7 x

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + 2 x^{2} + \frac{7 x}{4} - 1

y = c_{1} cos (2 x) + c_{2} sin (2 x) + 2 x^{2} + \frac{7 x}{4} - 1

y^{^{''}} - 4 y^{^{'}} = x

y^{^{''}} + 3 y = cos (3 x)

y^{^{''}} - 4 y^{^{'}} = e^{4 x}

y^{^{''}} - 11 y^{^{'}} + 24 y = 280 e^{t}

y^{^{''}} + 9 y = 5 sec (3 x)