Answer: The required solution of the given IVP is

Step-by-step explanation: We are given to find the solution of the following initial value problem :

Let
be an auxiliary solution of the given differential equation.
Then, we have

Substituting these values in the given differential equation, we have
![m^2e^(mx)-e^(mx)=0\\\\\Rightarrow (m^2-1)e^(mx)=0\\\\\Rightarrow m^2-1=0~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^(mx)\\eq0]\\\\\Rightarrow m^2=1\\\\\Rightarrow m=\pm1.](https://img.qammunity.org/2020/formulas/mathematics/college/d755uhyz0pky7y21keuh98l5v65seo8uc2.png)
So, the general solution of the given equation is
where A and B are constants.
This gives, after differentiating with respect to x that

The given conditions implies that

and

Adding equations (i) and (ii), we get

From equation (i), we get

Substituting the values of A and B in the general solution, we get

Thus, the required solution of the given IVP is
