Equating the two expressions for $t$ from Problems 1 and 2 we obtain the integral equation $$k(x,y,p) = \int_c^d G dx$$ To get rid of the integral, we differentiate both sides of the equation with respect to $x$. On the left hand side of the resulting equation we obtain the following expression (which might involve $x$, $y$, $p=\frac{dy}{dx}$ and $q=\frac{dp}{dx}=\frac{d^2y}{dx^2}$

(remember to separate different variables in a product with spaces or multiplication signs)
while on the right hand side (after applying the Fundamental Theorem of Calculus) we obtain

The resulting differential equation we obtained above is a separable differential equation in the variables $p$ and $x$. We can rewrite it in the form $$K(p)dp = L(x)dx$$ (with all numerical factors moved to the right hand side of the equation so that L(1)=10/20.) where
$K(p)$ =
$L(x)$ =