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

解

(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

解答ステップ

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

線形 ODE を解く:

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