You have
$$
\frac{d^2y}{dx^2} = 4 - \frac{15}{4} \sqrt{x}
$$
You can either rearrange that equation so that it looks like
$$
\frac{d^2y}{dx^2} + k \sqrt{x} = 4
$$
and identify what ##k## is, or use a more robust approach by substituting the ##\frac{d^2y}{dx^2}## you have found into that second equation,
$$
\left(4 - \frac{15}{4} \sqrt{x} \right) + k \sqrt{x} = 4
$$
and solve for ##k##.
Thread closed. The OP has been warned five times previously that homework-type questions must be posted in one of the forum sections devoted to homework questions.