Can anybody help me solve this differential equation?

Question

ivancsc1996 · Answer

$$f''(x)+f''(x)f(x)-f''(x)(f'(x))^{2}=(1+(f'(x))^{2})^{2}$$

anonymous · Answer

try factoring an f'' from the left side, it should then be a first order differential equation$$1+f(x)-(f(x))^{2}=1/f \prime \prime+2f \prime(x)^{2}/f \prime \prime+f'(x)^{4}/f''$$

ivancsc1996 · Answer

But remember that the term squared on the left side is f'(x), not f(x). The problem is that I dont know anything about differential equations more that separation of variables. I just got that equation through a physics problem and need the answer.

anonymous · Answer

are you looking for specific solutions or a sample equation for f(x)?

ivancsc1996 · Answer

An equation for f(x) is he solution isn't it?

anonymous · Answer

yes, but with most differential equations there are an infinite number of solution equations usually expressed f(x)=ce^tx+ke^tx, where c and k are both constants from -infinity to infinity.

ivancsc1996 · Answer

I would like the solutions with the two arbitrary constants. Please :)