I believe that I have worked the problem correctly to the point where I am, however I am not sure how to incorporate complex numbers into my answer?(adsbygoogle = window.adsbygoogle || []).push({});

The problem is :Make the substitution v = ln x to solve 4x^2 * y" + 8xy' - 3y = 0. Where " represents double prime, and ' represents prime.

This is my work so far:

v = ln x dv/dx = 1/x

dy/dx = dy/dv * dv/dx

dy/dx = dy/dv * 1/x

d"y/dx" = d/dx [dy/dv * 1/x] - dy/dv * 1/x^2

= 1/x * d/dx[dy/dv] - dy/dv * 1/x^2

= 1/x^2 * d"y/dv" - dy/dv * 1/x^2

Then plugging into the original equation:

4x^2[t/x^2 * d"y/dv" - dy/dv * 1/x^2] + 8x[dy/dv * 1/x] - 3y = 0

which can be broken down to

4d"y/dv" + 4dy/dv - 3y = 0

Substituting in R, i get 4r^2 + 4r - 3 = 0

This does not readily look factorable to me so I use the quadratic equation.

[-4 +- Square Root of (16 - 48)]/8

Here is where I run into the problem, does that turn into [-2 +- Square root of (8i)] / 4

It has been a while since I have dealt with complex numbers and I do not recall how to manipulate them.

If that is the correct equation, can anyone tell me how to finish the problem?

Thanks,

Josh

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# Homework Help: DE and Complex numbers

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