CPM Homework Help : APCALC Problem 10-21

Write the equation of the curve whose derivative at every point $(x, y)$ is $\frac { 3 x ^ { 2 } } { 2 y }$ and passes through the point $(2, 1)$ .

Step 1:

$2ydy=3x^2dx$

Step 2:

$\int2ydy=\int3x^2dx$

Step 3:

$y^2=x^3+C$

Step 4:

Use the given point to solve for $C$ .