Given that y1 (x) = t* is a known solution of the linear differential equation ²y" – 7ty + 16y = 0, t > 0 - Use reduction of order to find the general solution of the equation. O y = c¡t* In(t) + c2t4 O y = c1fª + c2f O y = c¡f* + c2e't O y = cirte + czr* N y = cjt + cɔt4
Given that y1 (x) = t* is a known solution of the linear differential equation ²y" – 7ty + 16y = 0, t > 0 - Use reduction of order to find the general solution of the equation. O y = c¡t* In(t) + c2t4 O y = c1fª + c2f O y = c¡f* + c2e't O y = cirte + czr* N y = cjt + cɔt4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Problem Statement:**
Given that \( y_1(x) = t^4 \) is a known solution of the linear differential equation
\[ t^2 y'' - 7t y' + 16y = 0, \quad t > 0 \]
Use reduction of order to find the general solution of the equation.
**Choices:**
- \( \circ \quad y = c_1 t^4 \ln(t) + c_2 t^4 \)
- \( \circ \quad y = c_1 t^4 + c_2 t^5 \)
- \( \circ \quad y = c_1 t^4 + c_2 e^{t} t^4 \)
- \( \circ \quad y = c_1 t^4 e^t + c_2 t^4 \)
- \( \circ \quad y = c_1 t + c_2 t^4 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94b5d9e5-a910-4586-8266-4b923c499ba5%2F42417fc1-29ad-4eef-8cbb-58a79d41cd37%2Fevxz3pe_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given that \( y_1(x) = t^4 \) is a known solution of the linear differential equation
\[ t^2 y'' - 7t y' + 16y = 0, \quad t > 0 \]
Use reduction of order to find the general solution of the equation.
**Choices:**
- \( \circ \quad y = c_1 t^4 \ln(t) + c_2 t^4 \)
- \( \circ \quad y = c_1 t^4 + c_2 t^5 \)
- \( \circ \quad y = c_1 t^4 + c_2 e^{t} t^4 \)
- \( \circ \quad y = c_1 t^4 e^t + c_2 t^4 \)
- \( \circ \quad y = c_1 t + c_2 t^4 \)
![**Problem: Solve the Differential Equation**
Solve the differential equation
\[
\frac{dy}{dx} + y \tan x = \cos x, \quad y(\pi) = -3\pi.
\]
**Options:**
- \( \circ \quad y = x \sin(x) + 2\pi \cos(x) \)
- \( \circ \quad y = x \sin(x) + \pi \cos(x) \)
- \( \circ \quad y = \pi x \cos(x) + x \cos(x) \)
- \( \circ \quad y = x \cos(x) + 2\pi \cos(x) \)
- \( \circ \quad y = \pi \sin(x) + x \sin(x) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94b5d9e5-a910-4586-8266-4b923c499ba5%2F42417fc1-29ad-4eef-8cbb-58a79d41cd37%2Fb1od7v2_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Solve the Differential Equation**
Solve the differential equation
\[
\frac{dy}{dx} + y \tan x = \cos x, \quad y(\pi) = -3\pi.
\]
**Options:**
- \( \circ \quad y = x \sin(x) + 2\pi \cos(x) \)
- \( \circ \quad y = x \sin(x) + \pi \cos(x) \)
- \( \circ \quad y = \pi x \cos(x) + x \cos(x) \)
- \( \circ \quad y = x \cos(x) + 2\pi \cos(x) \)
- \( \circ \quad y = \pi \sin(x) + x \sin(x) \)
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