Chapter 12: Q2P (page 611)

Solve $(22.9)$ to get $(22 .10)$ . If needed, see Chapter $(8)$ , Section 2. The given equation $(D + x) y_{0} = 0 toobtain y_{0} = e^{- \frac{x^{2}}{2}} .$

Short Answer

Expert verified

Solving, $(D + x) y_{0} = 0$ results $y_{0} = e^{- \frac{x^{2}}{2}}$ .

Step by step solution

Concept of Differential equation

Differential equations are equations that connect one or more derivatives of a function. This implies that their answer is a function.

Step 2:Solve the equations to obtain the solution

Determine equations for the solution as follows:

$\begin{matrix} (D + x) y_{0} = 0 \\ \Rightarrow \frac{d y_{0}}{d x} + x y_{0} = 0 \\ \Rightarrow \frac{d y_{0}}{d y_{0}} + x d x = 0 \\ \Rightarrow \log y_{0} + \frac{x^{2}}{2} = \log c \end{matrix}$

So, . $\Rightarrow y_{0} = c e^{\frac{- x^{2}}{2}}$

Let $y_{0} (0) = 1$ , then, $c = 1$ .

$y_{0} = e^{- \frac{x^{2}}{2}}$

Therefore, solving $(D + x) y_{0} = 0$ , results $y_{0} = e^{- \frac{x^{2}}{2}}$ .

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Solve $(22.9)$ to get $(22 .10)$ . If needed, see Chapter $(8)$ , Section 2. The given equation $(D + x) y_{0} = 0 toobtain y_{0} = e^{- \frac{x^{2}}{2}} .$

Short Answer

Step by step solution

Concept of Differential equation

Step 2:Solve the equations to obtain the solution

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Solve(22.9) to get(22.10) . If needed, see Chapter(8) , Section 2. The given equation(D+x)y0=0toobtainy0=e−x22.

Short Answer

Step by step solution

Concept of Differential equation

Step 2:Solve the equations to obtain the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Engineering Physics

Quantum Physics

Conservation of Energy and Momentum

Radiation

Work Energy and Power

Study anywhere. Anytime. Across all devices.

Solve $(22.9)$ to get $(22 .10)$ . If needed, see Chapter $(8)$ , Section 2. The given equation $(D + x) y_{0} = 0 toobtain y_{0} = e^{- \frac{x^{2}}{2}} .$