Saved Bookmarks
| 1. |
Solve the differential equation `x(dy)/(dx)+y=xcosx+sinx ,`given `y(pi/2)=1` |
|
Answer» `dy/dx+y/x=cosx+sinx/x` `dy/dx+yP(x)=q(x)` `P(x)=1/x` `q(x)=cosx+sinx/x` IF=`e^(intPdx)` IF=x `y*IF=intq(x)IFdx+C` `yx=int(cosx+sinx/x)x+C` `=xsinx+C` `xy=xsinx+C` `x=pi/2` `y=1` `C=0` `xy=xsinx` `y=sinx`. |
|