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.Com
Question 1046185: If and , find the value of b.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Applying implicit differentiation on , 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 , it follows that a = 1/2, and b = -1/2.
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