Solve the following diffrential equation

Question

3x²y''+11xy'-3y=8-3ln(x)

Answer 1

1xy'-3y=8-ln(x)

Solution

Let's make y the subject of the following

1xy' is the same as xy

Take out y(x-3)=8-ln(x)

Divide both sides by y

We have y=8-ln(X)/x-3

Using quotient rule

Let u=8-ln(x)and v= x-3

du/dx= -3/x

And dv/dx= 1

Combining

dy/dx= -3x+9-8-3ln(x)

= -3x-1-3lnx