Chapter 6: Q12E (page 332)

Find a general solution for the differential equation with x as the independent variable:
$y''' + 5 y'' + 3 y' - 9 y = 0$

Short Answer

Expert verified

The general solution for the differential equation with x as the independent variable is $y (x) = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} x e^{- 3 x}$

Step by step solution

Auxiliary equation:

Consider the equation . $y''' + 5 y'' + 3 y' - 9 y = 0$

The associated auxiliary equation is $r^{3} + 5 r^{2} - 3 r - 9 = (r - 1) {(r + 3)}^{2} = 0$ which has $r = - 3$ as a double solution and $r = 1$ as a simple solution.

General solution:

The general solution to the given equation is given by

$y (x) = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} x e^{- 3 x}$

Hence the final solution is $y (x) = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} x e^{- 3 x}$

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Find a general solution for the differential equation with x as the independent variable:
$y''' + 5 y'' + 3 y' - 9 y = 0$

Short Answer

Step by step solution

Auxiliary equation:

General solution:

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Find a general solution for the differential equation with x as the independent variable:y'''+5y''+3y'−9y=0

Short Answer

Step by step solution

Auxiliary equation:

General solution:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Find a general solution for the differential equation with x as the independent variable:
$y''' + 5 y'' + 3 y' - 9 y = 0$