Question

Find the solution of the differential equation that satisfies the given initial condition. (du)/(dt) = (2t + sec^2 t)/(2u), u(0) = -5

Answer 1

This ODE is separable:

`(\mathrm du)/(\mathrm dt)=(2t+\sec^2t)/(2u)`

`\implies2u\,\mathrm du=(2t+\sec^2t)\,\mathrm dt`

Integrating both sides gives

`u^2=t^2+\tan t+C`

Given that
`u(0)=-5`, we have

`(-5)^2=0^2+\tan0+C\implies C=25`

so that the particular solution to the IVP is

`u(t)^2=t^2+\tan t+25`

`\boxed{u(t)=√(t^2+\tan t+25)}`