求微分方程dy/dx+2y=e^x的通解．

求微分方程dy/dx+2y=e^x的通解．

∵P(x)=2 Q(x)=e^x ∴y=e^-∫P(x)dx[∫Q(x)dxe^∫P(x)dxdx+C]=e^-∫2dx[∫e^xe^∫2dxdx+C] =e^-2x[∫e^3xdx+C]=e^-2x[(1/3)e^3x+C]． 故原方程通解为 y=(1/3)e^x+Ce^-2x．