SOLUTION: If {{{y^2=1+sin x}}} and {{{y((d^2)y/d(x^2))+(dy/dx)^2+ay^2+b=0}}}, find the value of b.

Algebra ->  Test -> SOLUTION: If {{{y^2=1+sin x}}} and {{{y((d^2)y/d(x^2))+(dy/dx)^2+ay^2+b=0}}}, find the value of b.      Log On


   

Question 1046185: If y%5E2=1%2Bsin+x and y%28%28d%5E2%29y%2Fd%28x%5E2%29%29%2B%28dy%2Fdx%29%5E2%2Bay%5E2%2Bb=0, find the value of b.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Applying implicit differentiation on y%5E2=1%2Bsin+x, we get
2yy' = cosx
another application of implicit differentiation yields
2[(y')^2 +yy"] = -sinx
===> (y')^2 +yy" = -(sinx)/2
===> (y')^2 +yy" + (sinx)/2 = 0, or
yy" + (y')^2 + (sinx)/2 = 0.
Since y%5E2=1%2Bsin+x, it follows that a = 1/2, and b = -1/2.