- #1
Daniel5423
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Homework Statement
In my physics homework, I ran into a differential equation. I am attempting to solve this differential equation for y(x).
Homework Equations
y''[x] = -C/(y[x]^3) - y[x]
C is a constant
The Attempt at a Solution
dy^2/dx^2 = -C y[x]^-3 - y[x]
(1)/(-Cy[x]^-3 - y[x]) dy^2= dx^2
(-1/4)(ln(y^4 + C) dy = x dx
Now, I have to solve the integral for dy.
I was unable to find the integral for dy when it had a logarithm, so I manipulated the equation
ln(y^4 + C) dy = -4x dx
Now, use the e exponent.
(y^4 + C) e^dy = e^(-4x dx)
Now, do the integral.
(y^4 + C) e^y = e^-2x^2
Now, I can not solve for y in terms of x. If I try to use a natural logarithm to get rid of the e, it puts the other y term within the logarithm. I believe I did the differential equation incorrectly. Could someone please help me and give me a hint of what I did incorrectly? Thanks in advance.