题目 Problem Find the particular solution of the differential equation d2ydx2+2dydx+3y=27x2,\frac{\mathrm{d}^2y}{\mathrm{d}x^2}+2\frac{\mathrm{d}y}{\mathrm{d}x}+3y=27x^2,dx2d2y+2dxdy+3y=27x2, given that, when x=0x=0x=0, y=2y=2y=2 and dydx=−8\frac{\mathrm{d}y}{\mathrm{d}x}=-8dxdy=−8. [10] 题目中文翻译 求微分方程 d2ydx2+2dydx+3y=27x2\frac{\mathrm{d}^2y}{\mathrm{d}x^2}+2\frac{\mathrm{d}y}{\mathrm{d}x}+3y=27x^2dx2d2y+2dxdy+3y=27x2 的特解，已知当 x=0x=0x=0 时，y=2y=2y=2 且 dydx=−8\frac{\mathrm{d}y}{\mathrm{d}x}=-8dxdy=−8。 解答
