(d-2)^2y=8(e^2x+sin^2(x)+x^2)

Lösung

(d - 2)^{2} y = 8 (e^{2} x + sin^{2} (x) + x^{2})

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{2 x} \cdot \int - \frac{8 x ( e ^{2} x + sin ^{2} ( x ) + x ^{2} )}{e ^{2 x}} d x + e^{2 x} x \cdot \int \frac{8 ( e ^{2} x + sin ^{2} ( x ) + x ^{2} )}{e ^{2 x}} d x

Schritte zur Lösung

(d - 2)^{2} y = 8 (e^{2} x + sin^{2} (x) + x^{2})

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{2 x} \cdot \int - \frac{8 x ( e ^{2} x + sin ^{2} ( x ) + x ^{2} )}{e ^{2 x}} d x + e^{2 x} x \cdot \int \frac{8 ( e ^{2} x + sin ^{2} ( x ) + x ^{2} )}{e ^{2 x}} d x

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + e^{2 x} \cdot \int - \frac{8 x ( e ^{2} x + sin ^{2} ( x ) + x ^{2} )}{e ^{2 x}} d x + e^{2 x} x \cdot \int \frac{8 ( e ^{2} x + sin ^{2} ( x ) + x ^{2} )}{e ^{2 x}} d x

(d - 3)^{2} \cdot y = 2 e^{4 x}

(d^{2} - 4) \cdot y = x^{2}

y^{^{''}} + y^{^{'}} + 3 y = 9 x^{2} + 3

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

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