Chapter 8.7, Problem 1P

Solve the following differential equations by method (a) or (b) above.

$y^{\prime \prime }+y{y}^{\prime }=0.$ Find a solution satisfying each of the following sets of initial conditions. If your computer says there is no such solution, don’t believe it - do it by hand.

(a) $y(0)=5,y^{\prime }(0)=0$ (b) $y(0)=2,y^{\prime }(0)=-2$

(c) $y(0)=1,y^{\prime }(0)=-1$ (d) $y(0)=0,y^{\prime }(0)=2$