# Thread: (lny)^2 dy/dx = x^2 * y

1. ## (lny)^2 dy/dx = x^2 * y

Question:
Find the solution of the differential equation
which satisfies the initial condition .
?

My work:

(My work is attached and shows where I'm stuck which is basically on the step after having evaluated the integrals)

Any help would be greatly appreciated!

2. Originally Posted by s3a
Question:

Find the solution of the differential equation

which satisfies the initial condition .
?

My work:
(My work is attached and shows where I'm stuck which is basically on the step after having evaluated the integrals)

Any help would be greatly appreciated!

3. Originally Posted by s3a
Question:

Find the solution of the differential equation

which satisfies the initial condition .
?

My work:
(My work is attached and shows where I'm stuck which is basically on the step after having evaluated the integrals)

Any help would be greatly appreciated!
$\displaystyle \int \frac{(\ln(y))^2}{y}dy = \int x^2dx$
$\displaystyle \frac{(\ln(y))^3}{3} = \frac{x^3}{3} + c$