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First you have to have the absolute value isolated so the 2 has to be divided. Then set up the two cases and solve.
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
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