CPM Homework Help : APCALC Problem 10-56

Solve for $y$ if $\frac { d y } { d x } = \frac { x y } { \operatorname { ln } ( y ) }$ .

Step 1:

$\frac{\ln(y)}{y}dy=x dx$

Step 2:

Integrate. To integrate the left side of the equation, use substitution. Let $u = \ln(y)$ .

Step 2 Answer:

$\frac{1}{2}(\ln(y))^2=\frac{1}{2}x^2+C$

Step 3:

Solve for $y$ .