Solve differential equation

  • Thread starter DryRun
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  • #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?
 
Last edited:

Answers and Replies

  • #2
jgens
Gold Member
1,583
50
Is this answer correct?

It looks correct to me.
 

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