x(y^2+2xyy')=cos(xy^2) 细节

x(y^2+2xyy')=cos(xy^2) 细节
x(y^2+2xyy')=cos(xy^2)
细节

x(y^2+2xyy')=cos(xy^2) 细节
∵x(y^2+2xyy')=cos(xy^2)
==>xd(xy^2)/dx=cos(xy^2)
==>d(xy^2)/cos(xy^2)=dx/x
==>ln│(1+sin(xy^2))/cos(xy^2)│=ln│x│+ln│C│ (C是常数)
==>(1+sin(xy^2))/cos(xy^2)=Cx
==>1+sin(xy^2)=Cxcos(xy^2)
∴原方程的通解是1+sin(xy^2)=Cxcos(xy^2).