Try again < Previou You have answered 3 out of 4 parts correctly. Consider the differential equation: – 30x?y" – 12x( – 5)y + 12(x – 5)y= 0, x > 0. a. Given that yı(x) 3x is a solution, apply the reduction of order method to find another solution Y2 for which Y1 and y2 form a fundamental solution set. i. Starting with Yı, solve for w in yıw' + (2y1 + p(x)y1)w = 0 so that w(1) = 4. w(x) = 4e ii. Now solve for u where u': = w so that u(1) = -2. u(x) = -10e iii. Finally, write down y2 using the u that you found. Y2 (x) = -30xe +24x b. Find the particular solution corresponding to the initial conditions y(7) = 4 and y (7) = –3. Give your answer as y =... . Answer: y=3·-7.22343 ·x+0.646058 · –30e +24x 2.
Try again < Previou You have answered 3 out of 4 parts correctly. Consider the differential equation: – 30x?y" – 12x( – 5)y + 12(x – 5)y= 0, x > 0. a. Given that yı(x) 3x is a solution, apply the reduction of order method to find another solution Y2 for which Y1 and y2 form a fundamental solution set. i. Starting with Yı, solve for w in yıw' + (2y1 + p(x)y1)w = 0 so that w(1) = 4. w(x) = 4e ii. Now solve for u where u': = w so that u(1) = -2. u(x) = -10e iii. Finally, write down y2 using the u that you found. Y2 (x) = -30xe +24x b. Find the particular solution corresponding to the initial conditions y(7) = 4 and y (7) = –3. Give your answer as y =... . Answer: y=3·-7.22343 ·x+0.646058 · –30e +24x 2.
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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Transcribed Image Text:Try again
< Previou
You have answered 3 out of 4 parts correctly.
Consider the differential equation:
– 30x?y" – 12x( – 5)y + 12(x – 5)y= 0,
x > 0.
a. Given that yı(x)
3x is a solution, apply the reduction of order method to find another solution
Y2
for which
Y1
and y2
form a fundamental solution set.
i. Starting with Yı, solve for w in yıw' + (2y1 + p(x)y1)w = 0 so that w(1) = 4.
w(x) =
4e
ii. Now solve for u where u':
= w so that u(1) = -2.
u(x) =
-10e
iii. Finally, write down y2 using the u that you found.
Y2 (x) =
-30xe
+24x
b. Find the particular solution corresponding to the initial conditions y(7) = 4 and y (7) = –3. Give your answer as y =... .
Answer:
y=3·-7.22343 ·x+0.646058 · –30e
+24x
2.
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