y'=y/(1+x^2)1/y dy=1/(1+x^2)dx两滚亏边积分，得∫1/大樱神y dy=∫1/颂段(1+x^2)dxln|y|=arctanx+ln|c|y=ce^(arctanx)π=ce^0c=πy=πe^(arctanx)y(1)=πe^(π/4)选D
