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Find the general solution for
Solution:
Consider the given equation above
Express y' as dy/dx as follows
By separation of variables, transpose dx and (e2x + 4) to the right side of the equation and y to the left side of the equation, we have
Did you notice that the right side of an equation cannot be integrated by simple integration? The differential of e2x + 4 is 2e2xdx and 2e2x is missing at the numerator. Because of this, we have to use the algebraic substitution as follows
Let
So that
The value of dx is
Hence, the above equation becomes
By separating the partial fractions, we can solve for the values of A and B as follows
Equate x0: 
Equate x:
Substitute the values of A and B to the above equation, we have
Take the inverse natural logarithm on both sides of the equation, we have
but
Hence, the above equation becomes
Therefore, the general solution is
