(d^2-4d+4)y=x^2+e^x+cos^2(x)

解

(d^{2} - 4 d + 4) y = x^{2} + e^{x} + cos^{2} (x)

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

解答ステップ

(d^{2} - 4 d + 4) y = x^{2} + e^{x} + cos^{2} (x)

線形 ODE を解く:

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

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