Is it possible to solve this type of differential equation?

While solving a calculus problem, I encountered a type of differential equation that I had never seen before. This is the differential equation:

$$f'(x)=\frac { x }{ f(x) } -\frac { 1 }{ f(1) }$$

Is this equation solvable or not. If it is, could someone please explain how to solve it.

• $\frac1{f(1)}$ is just a number (that you'll want to make sure is equal to $\frac1{f(1)}$ at the end). Let's call it $a$. Then we can literally ask a computer if the equation is solvable and find out the solution, and what named category of differential equation this falls under. May 31 '19 at 23:19

$$f'(x)=\frac{x}{f(x)}-\frac{1}{f(1)}$$ $$f'(x)f(x)+\frac{f(x)}{f(1)}=x$$ Now this is a non-linear first order ODE. They do not always have a nice solution