Linear Equations: Answer to Example 2
Example: Solve the following initial value problem for t > 0
Answer: This is a linear equation. Let us follow these
steps for solving such equations:

 1.
 We have to divide by 2t
 2.
 We get the integration factor u(t) by
 3.
 The general solution is given by
.
Since
Therefore, we have
 4.
 The solution to the given initial value problem may be obtained by using the initial condition y(2)=4. We have
,
which gives . Therefore, the solution is
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