Calculus 3 (Differential equation)

Question

Prove that each equation is a solution of the given differential equation:

In y = C₁e^x + C₂e^-x ; yy’’- (y’)² = y² In y

Answer 1

y'/y = C₁e^x - C₂e^-x; [y''y - (y')²]/y² = C₁e^x + C₂e^-x;

From here yy'' - (y')² = y²lny. So, to prove we differentiate given function implicitly 2 times