Slope fields and Euler’s method practice question 6

There are two jobs: confirm the family satisfies the equation, then let $y(0) = 4$ choose $C$. The square root of an expression in $t$ is a composition: which rule differentiates it?

By the chain rule, $\dfrac{d}{dt}\sqrt{t^{2} + C} = \dfrac{2t}{2\sqrt{t^{2} + C}}$. Compare with $\dfrac{t}{y}$.

The initial condition says $\sqrt{0 + C} = 4$. Solve for $C$ before evaluating at $t = 3$.