Sometimes, the DE might not be in the variableseparable (VS) form; however, some manipulations might be able to transform it to a VS form. Lets see how this can be done. Consider the DE
This is obviously not in VS form. Observe what happens if we use the following substitution in this DE:
Thus, the DE transforms to
which is clearly a VS form. Integrating both sides, we obtain
This is the required general solution to the DE.
From this example, you might be able to infer that any DE of the form
is reducible to a VS form using the technique described. Let us confirm this explicitly. Substitute
Thus, our DE reduces to
which is obviously in VS form, and hence can be solved.
Example: 1  
Solve the DE 
Solution: 1  Steps Involved: 2 
Step1
Substituting we have
and thus the DE reduces to

Step2
Integrating, we have

Example: 2  
Solve the DE 
Solution: 2  Steps Involved: 3 
Step1
Again, the substitution will reduce this DE to the following VS form:

Step2
Integrating, we have

Step3
To evaluate the integral on the LHS, we use the substitution which gives . Thus,
