The first-order equation\

2x^(2)u(du)/(dx)+xu^(2)+2=0

\ is an example of an "isobaric" equation for which there's a value of

m

(called the weight)\ such that

u

has the same dimension as

x^(m)

. The allows the equation to be rendered\ separable with the substitution of the dimensionless

v(x)=u(x)/(x^(m))

in place of

u

.\ a. (10 points) Confirm that the equation is isobaric by substituting

v(x)

and determining\ the value of

m

for which the equation is separable.

2. The first-order equation 2x2udxdu+xu2+2=0 is an example of an "isobaric" equation for which there's a value of m (called the weight) such that u has the same dimension as xm. The allows the equation to be rendered separable with the substitution of the dimensionless v(x)=u(x)/xm in place of u. a. (10 points) Confirm that the equation is isobaric by substituting v(x) and determining the value of m for which the equation is separable