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

Torque and Rotational Motion

Measurements

Further Mechanics and Thermal Physics

Space Physics

Scientific Method Physics

Engineering Physics

Study anywhere. Anytime. Across all devices.

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