Вопрос

3 y^prime prime-y^prime-2 y=0

4.7 (254 Голоса)

Карен

Экспертная проверка

мастер · Репетитор 5 лет

To solve the given differential equation

, we can use the characteristic equation method.Step 1: Write the characteristic equation.The characteristic equation is obtained by substituting

into the differential equation. This gives us:

Step 2: Solve the characteristic equation.We can solve the quadratic equation

using the quadratic formula:

where

, and

.Substituting these values, we get:

So, the roots are:

Step 3: Write the general solution.The general solution to the differential equation is given by:

where

and

are arbitrary constants.Substituting the values of

and

, we get:

Therefore, the general solution to the differential equation

is: