(d^2-1)y=xsin^3(x)+cos(x)

Lösung

(d^{2} - 1) y = x sin^{3} (x) + cos (x)

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

Schritte zur Lösung

(d^{2} - 1) y = x sin^{3} (x) + cos (x)

Solve linear ODE:

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

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

(d^{4} + 8 d^{2} + 16) \cdot y = - 2

(d^{2} + 3 d + 2) y = e^{2} x + sin (x)

y^{^{''}} - 4 y^{^{'}} + 5 y = x^{2} e^{3} x

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

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