Q24E - Fundamentals Of Differential Equations And Boundary Value Problems

Question

In Problems 22–25, use the method described in Problem 21 to find a general solution to the given equation.

24. 3z' + 11z = 0

Step-by-Step Solution

Answer

The general solution is $z\left(t\right)=c{e}^{-\frac{11}{3}t}$.

Step 1: Substitute z = e rt

The given differential equation is 3z' + 11z = 0

Substitute z = e^rt and z' = re^rt,

3(re^rt) + 11(e^rt) = 0

    (3r + 11)(e^rt) = 0

            3r + 11 = 0

Therefore,

$r=-\frac{11}{3}$

Step 2: Find the general solution.

Therefore, the general solution is $z\left(t\right)=c{e}^{-\frac{11}{3}t}$.