高等数学求通解详细点

显示全部楼层 · 2012-10-11 16:36:02

解：设y'=p，则y''=dp/dx=(dp/dy)(dy/dx)=pdp/dy
代入原方程，得pdp/dy=50sin3ycosy
==>pdp=50sin3ycosydy
==>pdp=50sin3yd(siny)
==>p2=25(siny)^4+C1(C1是积分常数)
==>y'2=25(siny)^4+C1
∵y(1)=π/2，y'(1)=5...

千问 · 2012-10-11 16:36:02

微分方程的题目。令y'=Py''=dp/dx=(dp/dy)(dy/dx)=p(dp/dy)pdp=50sin^3ycosydyp^2=25sin^4y+c1根据题设p在y=π/2时值为5，故c1=0故p=5sin^2y1/sin^2ydy=5dx-coty=5x+c2因为y(1)=π/2，0=5+c2，故c2=-5得co...