- #1

DryRun

Gold Member

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**Homework Statement**

Solve [tex]\frac{dy(t)}{dt}+2ty(t)=5t

\\y(0)=1[/tex]

**The attempt at a solution**

Since this is a 1st order ODE, i find the integrating factor,

[tex]μ(t)=e^{\int P(t).dt}

\\P(t)=2t

\\Q(t)=5t

\\μ(t)=e^{t^2}

[/tex]

Using formula:

[tex]\frac{dμy}{dt}=μQ[/tex]

Integrating both R.H.S. and L.H.S.:

[tex]μy=\int e^{t^2}.5t\,.dt

\\μy=\frac{5}{2}e^{t^2}+A

\\y=\frac{5}{2}+\frac{A}{e^{t^2}}

[/tex]

Using y(0)=1

When t=0, y=1

[itex]1=\frac{5}{2}+A[/itex], so A=1-(5/2)=-3/2

Therefore, the particular solution is: y=(5/2)-(3/2) which gives y=1.

Is this answer correct?

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