Chapter 4: Q4.3-18E (page 172)

Find a general solution. $2 y " + 13 y' - 7 y = 0$

Short Answer

Expert verified

The general solution of the given equation $2 y " + 13 y' - 7 y = 0$ isrole="math" localid="1654072917909" $y (t) = c_{1} e^{\frac{1}{2} t} + c_{2} e^{- 7 t}$ .

Step by step solution

Differentiate the value of y.

Given differential equation is $2 y " + 13 y' - 7 y = 0 .$

Let $y = e^{it} .$

Therefore,

$\begin{matrix} y' (t) = r e^{tt} \\ y'' (t) = r^{2} e^{rt} \end{matrix}$

Finding the roots of the auxiliary equation.

Then the auxiliary equation is $2 r^{2} + 13 r - 7 = 0 .$

Solve the equation to obtain the roots of the auxiliary equation.

$r = \frac{- 13 \pm \sqrt{13^{2} - 4 \times 2 \times - 7}}{2 \times 2} r = \frac{- 13 \pm \sqrt{169 + 56}}{4} r = \frac{- 13 \pm \sqrt{225}}{4} r = \frac{- 13 \pm 15}{4} r = \frac{1}{2} or r = - 7$

Final answer.

Therefore, the general solution is $y (t) = c_{1} e^{\frac{1}{2} t} + c_{2} e^{- 7 t}$ .

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Find a general solution. $2 y " + 13 y' - 7 y = 0$

Short Answer

Step by step solution

Differentiate the value of y.

Finding the roots of the auxiliary equation.

Final answer.

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Find a general solution.2y"+13y'-7y=0

Short Answer

Step by step solution

Differentiate the value of y.

Finding the roots of the auxiliary equation.

Final answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Calculus

Pure Maths

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Find a general solution. $2 y " + 13 y' - 7 y = 0$