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noname [10]
3 years ago
13

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

= -5
Mathematics
1 answer:
Anvisha [2.4K]3 years ago
6 0

This ODE is separable:

\dfrac{\mathrm du}{\mathrm dt}=\dfrac{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)=\sqrt{t^2+\tan t+25}}

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