ylnx - xy' = 0
First we will
rewrite the equations.
ylnx =
xy'
==> ylnx = x
*dy/dx
In solving differential equation, out first priority
is to isolate x an y terms on different sides.
Then we will
multiply both sides by dx and divide by
xdy
==> lnx/x) dx =
dy/y
Now let us integrate both
sides:
==> intg (lnx/x) dx = intg
dy/y
Let u= lnx
==> du
= 1/x dx
==> x du =
dx
==> intg u/x * xdu = ln
y
==> intg u du = ln
y
==> ln y = u^2 /2 +
C
Now subsitute with u= ln
x
==> ln y = (lnx)^2 /2 +
C
==> y= e^(1/2)(lnx)^2 +
C
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