A problem in differential equation

[AlonsoMcLaren]

http://www.math.upenn.edu/ugrad/calc/m114/exams/07cMath114FinalExam.pdf

Problem 5

 

[lurflurf]

by the chain rule
$$\frac{d}{dx}=\frac{\partial}{\partial x}+\frac{dy}{dx}\frac{\partial}{\partial y}$$

 

[AlonsoMcLaren]

What to do next...

 

[lurflurf]

$$\frac{d^2 y}{dx^2}=\frac{df}{dx}=\frac{\partial f}{\partial x}+f \frac{\partial f}{\partial y}$$

the values of f and its first order partials are known from the problem statement