Solve the following initial value problem: tdy/dt+5y=5t with y(1)=8. Put the problem in standard form. Then...

Solve the following initial value problem: tdy/dt+5y=5t with y(1)=8.

Put the problem in standard form.

Then find the integrating factor, ρ(t)=

and finally find y(t)=

Solutions

Expert Solution

This is the linear differential equation of first order of the standard form: (dy/dt) + P(t)y=Q(t). The integrating factor = e. The general solution is given by:

= . Then applying initial condition y(1)=8 we get the particular solution.

Colby Messinger answered 9 months ago

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