General Solution of differential equation (x – y^2)dx +y(5x + y^2)dy

The general solution of the differential equation is:

1. 
2. 
3. 
4. 

Solution:

Find the general solution of a given differential equation using the substitution method.

Given,

… (1)

Let

On differentiation, we get

Then, equation (1) becomes

… (2)

Now, Substitute t = vx

On differentiation, we get

Then, equation (2) becomes

… (3)

Now, integrate equation (3)

Integrate using partial faction

On Partial Fraction,

… (4)

Now,

Then equation (4) becomes

Final Answer:

Hence, Option (A) is correct.