Solving circuit using Laplace Transforms

[perplexabot]

Hi all. I need to find the voltage across the inductor. I begin by solving for the current in the inductor. I first solved a circuit using differential equations (with mathematica) and achieved an answer for current in inductor of: iL(t) = E^(-5 t) (-0.75 + 1.25 E^(4 t)

Later, I tried to solve the same circuit using Laplace transforms and was not able to yield the same answer (or anything close). The original circuit and my approach for solving the circuit using Laplace transforms is attached as a pdf file. In the pdf file, I am attempting to solve for the current in the inductor. I get an equation for iL(s), however, when I take the inverse laplace, the answer looks nothing like my diff-eq iL(t). Please let me know where I am going wrong. Hints are preferred over answers. Thank you.

 

[the_emi_guy]

In your loop 2 equation the voltage drop across inductor should be (i2)sL.

 

[perplexabot]

In your loop 2 equation the voltage drop across inductor should be (i2)sL.

WOW, you are so right. I can't believe I didn't see that. Thank you so much. I will give it another go. Hopefully I will not run into another error. Thanks again.

 

[perplexabot]

Thanks the_emi_guy. That simple fix gave me the exact answer.

 

[the_emi_guy]

You're welcome

 

[perplexabot]

I am now trying to solve the circuit by hand using differential equations. I have attempted it twice and went over it many times but have not achieved the correct answer (i am close though). I may upload my attempt tonight and hopefully you (or someone else) may help me with that too.