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(6) Solve the following ODE +x dy + (12x2 - v2 )y = 0 using a substitution of the form z = Ax dx dx

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(6) Solve the following ODE +x dy + (12x2 - v2 )y = 0 using a substitution of the form z = Ax dx dx SOLUTION: Substituting directly gives Z + Z dy + (z2 - v2 )y = 0 dz2 dz Note that dx = dz/ 1 Substituting into the original ODE gives y(z) = AJ, (z) + BY, (z) v(x) = AJ (Ax) + BY, (1x)

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