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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