What am I doing wrong? - Linear Differential Equations

[lelandsthename]

What am I doing wrong?? - Linear Differential Equations

Homework Statement

Hi everyone, the problem I have is listed under my attempt (I hope it's ok that I pasted it): to solve the below linear differential equation with the initial condition y(1)=1

Homework Equations

P(x) and Q(x) linear differential equation solution method

The Attempt at a Solution

Plugging in for 1=y and 1=x to solve for c has yielded me crazy results after i plugged in y^(-2). I got both c=6/7 and c=-1/6 but neither are the correct answer (this problem is listed on a program that allows me to check my answer) can anyone help me explain if I did a step wrong or if I am solving for C wrong??

Thanks!

 

[HallsofIvy]

I don't know why you say "crazy results". If y= 1, then z= 1 also so your last equation becomes 1= 1/7 + C and C= 6/7 is the only result.

y^-2= -(1/7)x^-4+ (6/7)x^-18 gives

y^2= \frac{1}{-(1/7)x^{-4}+ (6/7)x^{-18}}= \frac{-7}{x^{14}- 6}

 

[lelandsthename]

Well the crazy results come when i plug my answer into y=. The program keeps telling me that I am incorrect with
\sqrt{7x^4}+((7x^{18})/6)
(that's to the 18th)