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Example 1

Find the general solution of the equation

y' + 3t-1v = t2, t > 0.

Then find the particular solution with the initial value y(1) = ½.

Step 1

The corresponding homogeneous equation is x' + 3t-1x = 0. From Example 2 in Section 14.2, a particular solution is

x = t-3.

Step 2

14_differential_equations-61.gif

14_differential_equations-62.gif

Step 3

The general solution is y = vx + Cx, or y = (1/6)t3 + Ct-3.

Step 4

y(1) = ½ = (1/6)13 + C1-3, c = ⅓.

The required particular solution (Figure 14.3.1) is

y = (i)t3 + (i)r3.

14_differential_equations-63.gif

Figure 14.3.1 Example 1
Home Differential Equations First Order Linear Equations Examples Example 1

Last Update: 2006-11-17