Q14P Verify (7.19) and (7.20).聽; wri... [FREE SOLUTION]

Chapter 8: Q14P (page 436)

Verify (7.19) and (7.20).; write the first equation of (7.19) as $x D_{X} = D_{Z}$ , and find ${D^{2}}_{Z}$ .

Short Answer

Expert verified

Hence proved

$x^{2} \frac{d^{2} y}{d x^{2}} = \frac{d^{2} y}{d z^{2}} - \frac{d y}{d z} a_{2} \frac{d^{2} y}{d x^{2}} + (a_{1} - a_{2}) \frac{d y}{d z} + a_{0} y = f (e^{z})$

Step by step solution

Given information

It is given that,

$d x = e^{z} z = l n 鈦� x \frac{d z}{d x} = \frac{1}{x}$

Differential equation

Definition: A differential equation is an equation that relates one or more unknown functions and their derivatives.

Write expression for equation (7.19) & (7.20)

Write the expression for equation (7.19).

$x^{2} \frac{d^{2} y}{d x^{2}} = \frac{d^{2} y}{d z^{2}} - \frac{d y}{d z} 鈥� (1)$

Write the expression for equation.

$a_{2} \frac{d^{2} y}{d x^{2}} + (a_{1} - a_{2}) \frac{d y}{d z} + a_{0} y = f (e^{z}) 鈥� . . . (2)$

Prove equation (7.19)

Now,

Prove equation (7.20)

Now,

$a_{2} x^{2} \frac{d^{2} y}{d x^{2}} + a_{1} x \frac{d y}{d x} + a_{0} y = f (x) a_{2} (\frac{d^{2} y}{d z^{2}} - \frac{d y}{d z}) + a_{1} \frac{d y}{d z} + a_{0} y = f (e^{z}) a_{2} \frac{d^{2} y}{d x^{2}} + (a_{1} - a_{2}) \frac{d y}{d z} + a_{0} y = f (e^{z})$

Therefore, the proof for equation (7.19) and (7.20) is stated above.

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91影视

Verify (7.19) and (7.20).; write the first equation of (7.19) as $x D_{X} = D_{Z}$ , and find ${D^{2}}_{Z}$ .

Short Answer

Step by step solution

Given information

Differential equation

Write expression for equation (7.19) & (7.20)

Prove equation (7.19)

Prove equation (7.20)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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91影视

Verify (7.19) and (7.20).; write the first equation of (7.19) as xDX=DZ, and find D2Z.

Short Answer

Step by step solution

Given information

Differential equation

Write expression for equation (7.19) & (7.20)

Prove equation (7.19)

Prove equation (7.20)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Astrophysics

Fluids

Rotational Dynamics

Radiation

Medical Physics

Solid State Physics

Study anywhere. Anytime. Across all devices.

Verify (7.19) and (7.20).; write the first equation of (7.19) as $x D_{X} = D_{Z}$ , and find ${D^{2}}_{Z}$ .