y^{'''}+4y^{''}-9y^'-36=x^2-4

Lösung

y^{^{'''}} + 4 y^{^{''}} - 9 y^{^{'}} - 36 = x^{2} - 4

y = c_{1} + c_{2} e^{(- 2 + 13) x} + c_{3} e^{(- 2 - 13) x} - \frac{x ^{3}}{27} - \frac{4 x ^{2}}{81} - \frac{2642 x}{729}

Schritte zur Lösung

y^{'''} (x) + 4 y^{''} (x) - 9 y^{'} (x) - 36 = x^{2} - 4

Solve linear ODE:

y = c_{1} + c_{2} e^{(- 2 + 13) x} + c_{3} e^{(- 2 - 13) x} - \frac{x ^{3}}{27} - \frac{4 x ^{2}}{81} - \frac{2642 x}{729}

y = c_{1} + c_{2} e^{(- 2 + 13) x} + c_{3} e^{(- 2 - 13) x} - \frac{x ^{3}}{27} - \frac{4 x ^{2}}{81} - \frac{2642 x}{729}

y^{^{''}} + y = \frac{1}{( cos ( x ) )}

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

y^{^{''}} + 8 y^{^{'}} + 16 y = x

5 y^{^{''}} + 6 y^{^{'}} + 25 y = 3 cos (2 t)

y^{^{''}} - 6 y^{^{'}} + 34 y = 25 e^{3 t}, y (0) = 1