- #1
checkmatechamp
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Homework Statement
x*e^(y/x) + y dx = xdy, y(1) = 0
Homework Equations
The Attempt at a Solution
To solve, I divide everything by x dx to put everything in terms of v.
e^v + v = dy/dx
dy/dx = x dv/dx + v
e^v + v = x dv/dx + v
e^v = x dv/dx
e^v / dv = x/dx
Flip both sides.
e^-v dv = 1/x dx
Integrate both sides
-e^-v = ln|x| + c
-e^(-y/x) = e^(ln|x| + c)
-e^(-y/x) = x * e^c
-e^(-y/x) = cx
ln(-e^(-y/x)) = ln(cx)
ln(e^(x/-y)) = ln(cx)
-x/y = ln(cx)
1/y = -ln(cx)/x
y = -x/(ln(cx))
Is that the correct explicit form? Would it make it easier if I used the initial condition to find c, and then attempted to put it in explicit form, or not?