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# Convert first order system into a single second order ODE

dx/dt = 4x - y
dy/dt = 2x + y + t^2
x(0)=0 and y(0)=1.

The question says to solve this by first converting the two first orders into a single second order equation.

Any hints??

Thanks
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InteractiveMind
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1 Solution

Commented:
a hint
try using       dy/dt = (dy/dx)(dx/dt)

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Author Commented:
Hmm This definitely turns it into a second order?
What form does the second order take? (I'm wondering if I need to try and eliminate that t^2 term in the process)

Thank you
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Commented:
I have been ignoring the t term unjustifyably. I will have to go back to the drawing board
Sorry
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Commented:
This reminds me of my school days.

Differentiate the first equation with respect to t. Then use the first equation and the resultant differential equation to eliminate a variable in the second equation. Which variable that would be would be telling!
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Author Commented:
Wonderful. Thanks :)
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