(d^2+d-2)y=1+x-x^2

Lösung

(d^{2} + d - 2) y = 1 + x - x^{2}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2}

Schritte zur Lösung

(d^{2} + d - 2) y = 1 + x - x^{2}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{x ^{2}}{2}

(d^{3} + 2 d^{2} - 3 d) \cdot y = x \cdot e^{3 x}

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

(d^{2} - 2 d + 5) y = 5

d \cdot g (x) = 2 x + 1

4 y^{^{''}} + 4 y^{^{'}} + y = cos (t)