Solving an equation with a parameter and a derivative

[homeworkhelpls]

TL;DR Summary

For 3(i)(b) does anyone know how to find the value of k?

idk how to start after finding the second derivative

 

[DrClaude]

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 $k$.

 

[Mark44]

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.