# What am I doing wrong? - Linear Differential Equations

1. Oct 22, 2008

### lelandsthename

What am I doing wrong?? - Linear Differential Equations

1. The problem statement, all variables and given/known data
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

2. Relevant equations
P(x) and Q(x) linear differential equation solution method

3. 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!

Last edited: Oct 23, 2008
2. Oct 23, 2008

### HallsofIvy

Staff Emeritus
Re: What am I doing wrong?? - Linear Differential Equations

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

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

3. Oct 23, 2008

### lelandsthename

Re: What am I doing wrong?? - Linear Differential Equations

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)