(D^4+D^2)y=x^2+2x+4

解答

(D^{4} + D^{2}) y = x^{2} + 2 x + 4

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + \frac{x ^{4}}{12} + \frac{x ^{3}}{3} + x^{2}

求解步骤

(D^{4} + D^{2}) y = x^{2} + 2 x + 4

求解线性方程:

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + \frac{x ^{4}}{12} + \frac{x ^{3}}{3} + x^{2}

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + \frac{x ^{4}}{12} + \frac{x ^{3}}{3} + x^{2}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 12 y = (x + 1) e^{x}

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

y^{^{''}} - 12 y^{^{'}} + 36 y = 12 e^{6 x}

y^{^{''}} - 4 y^{^{'}} = e^{x}

4 \cdot y^{^{''}} - 11 \cdot y^{^{'}} - 3 y = 5 \cdot e^{3 x}