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Chapter 8: Q 13-8MP (page 466)

Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

Short Answer

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Step by step solution

Given information.

The given function is

Differential equation.

Find the complimentary function of the differential equation.

Find the particular solution.

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Most popular questions from this chapter

Solve $(12.3)$ if $G = 0$ and $d G / d t = 0$ at $t = 0$ to obtain (12.5). Hint: Use L28 and L3 to find the inverse transform.

Use the methods of this section to solve the following differential equations. Compare computer solutions and reconcile differences.

$y' = c o s (x + y)$

Hint: Let $u = x + y$ ; then $u' = 1 + y'$ .

Find the orthogonal trajectories of each of the following families of curves. In each case, sketch or computer plot several of the given curves and several of their orthogonal trajectories. Be careful to eliminate the constant from $y'$ for the original curves; this constant takes different values for different curves of the original family, and you want an expression for $y'$ which is valid for all curves of the family crossed by the orthogonal trajectory you are trying to find. See equations $(2.10)$ to $(2.12)$ .

${(y - 1)}^{2} = x^{2} + k$

Use L28 to find the Laplace transform of

$f (t) = {\begin{cases} s i n (t - π / 2), & t > π / 2 . \\ 0, & t < π / 2 . \end{cases}$

For each of the following differential equations, separate variables and find a solution containing one arbitrary constant. Then find the value of the constant to give a particular solution satisfying the given boundary condition. Computer plot a slope field and some of the solution curves.

1. $xy' = y, y = 3$ , when $x = 2$

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Question: Identify each of the differential equations in Problems 1to 24 as to type (for example, separable, linear first order, linear second order, etc.), and then solve it.

Short Answer

Step by step solution

Given information.

Differential equation.

Find the complimentary function of the differential equation.

Find the particular solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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