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)=

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 1 year ago

Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0)...

Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0) = 0, y(0) = 0

Solve the following initial value problem. y(4) − 5y′′′ + 4y′′ = x, y(0) = 0, y′(0) ...

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6. Consider the initial value problem dy/ dt = t ^2 y , y(1) = 1...

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Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...

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