(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Going through a book on Numerical Methods, it states,

[tex]y' = 4e^{0.8x}-0.5y[/tex]

has the analytical solution,

[tex]y= \dfrac{4}{1.3}(e^{0.8x}-e^{-0.5x})+2e^{-0.5x}[/tex]

2. Relevant equations

This is of the form,

[tex]y'+p(x)y=q(x)[/tex]

Should I use an Integrating Factor to solve the Linear ODE?, i.e. use an integrating factor [tex]\mu(x)=e^{\int{p(x)dx}}[/tex]

[tex]\mu(x)\left[y'+p(x)y\right]=\mu(x)q(x)[/tex]

[tex]\left(\mu(x)y\right)'=\mu(x)q(x)[/tex]

[tex]\mu(x)y=\int{\mu(x)q(x)dx+C}[/tex]

...and divide through by [tex]\mu(x)[/tex] ???

3. The attempt at a solution

[tex]\mu(x)=e^{\int{p(x)dx}}=e^{0.5x}[/tex]

thus,

[tex]e^{0.5x}y=4\int{e^{0.8x}e^{0.5x}dx+C}[/tex]

and it is given: y(0) = 2

Any pointers? Dick, your help would be much appreciated once again!

Thanks and happy new year to all as well,

Cheers

Mike

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# Homework Help: Another First-Order ODE Question

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