Implicit solutions to differential equations Ordinary differential equations are often of the form $f^{'}(x)=F(f(x),x)$. Solutions to such equations are functions that satisfy them and are differentiable.
If we integrate both sides of the equation we get $f(x)=f(0)+\int_{0}^{x}F(f(t),t)dt$, which looks like a solution but on the other hand we can also view it as an equivalent equation. 
Which of those two things is it, is it both? 

Both equations possibly define a function, but in an implicit way. A solution needs to be explicit.
$f'(x)=f(x)$ is an equation, $f(x)=e^x$ is a solution.
