Chapter 6: Q22E (page 332)

Find a general solution for the given linear system using the elimination method of Section 5.2.
$\begin{array}{l} \frac{d^{2} x}{d t^{2}} - x + 5 y = 0 \\ 2 x + \frac{d^{2} y}{d t^{2}} + 2 y = 0 \end{array}$

Short Answer

Expert verified

_{$y (t) = c_{1} \cos (2 x) + c_{2} \sin (2 x)$ The solution is}

Step by step solution

Elimination method

In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Solving linear system using the elimination method:

We will do the following question on the basis of solving linear system using the elimination method;

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Find a general solution for the given linear system using the elimination method of Section 5.2.
$\begin{array}{l} \frac{d^{2} x}{d t^{2}} - x + 5 y = 0 \\ 2 x + \frac{d^{2} y}{d t^{2}} + 2 y = 0 \end{array}$

Short Answer

Step by step solution

Elimination method

Solving linear system using the elimination method:

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Find a general solution for the given linear system using the elimination method of Section 5.2.d2xdt2−x+5y=02x+d2ydt2+2y=0

Short Answer

Step by step solution

Elimination method

Solving linear system using the elimination method:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Find a general solution for the given linear system using the elimination method of Section 5.2.
$\begin{array}{l} \frac{d^{2} x}{d t^{2}} - x + 5 y = 0 \\ 2 x + \frac{d^{2} y}{d t^{2}} + 2 y = 0 \end{array}$