calculus II separable equations

Question

Find the solution to the differential equation dy/dx=3xy/(lny)⁸ which passes through the point (0,e). Express your answer as lny=

Answer 1

(ln⁸y/y) dy = 3x dx

ln⁹y = (3/2)x² + C

at (0,e) C=1

ln y = [(3/2)x² + 1]^1/9