Show that each of the functions defined in (A) is a solution of the corresponding differential equation in (B) for each number, subject to the given conditions. A B y = C,e* + Ce* 2. y = C,e* + Ce* + x – 4 3. y = Ce* + C,e2x + x²e* y" - y = 0 y" - y = 4 - X y" - 3y' + 2y = 2e*(1 – x) 1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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This is a calculus about differential equations.
Show that each of the functions defined in (A) is a solution of the corresponding differential
equation in (B) for each number, subject to the given conditions.
A
B
y = C,e* + C,e*
2. у%3D Се* + C,e* + x - 4
3. y = Ce* + C,e²x + x²e*
4. (1- х)у* %3 х
5. y = e*(1+ x)
y" - y = 0
y" - y = 4 - X
y" - 3y' + 2y = 2e*(1 – x)
2x?y' = y(y + 3x*)
y" – 2y' + y = 0
1.
Transcribed Image Text:Show that each of the functions defined in (A) is a solution of the corresponding differential equation in (B) for each number, subject to the given conditions. A B y = C,e* + C,e* 2. у%3D Се* + C,e* + x - 4 3. y = Ce* + C,e²x + x²e* 4. (1- х)у* %3 х 5. y = e*(1+ x) y" - y = 0 y" - y = 4 - X y" - 3y' + 2y = 2e*(1 – x) 2x?y' = y(y + 3x*) y" – 2y' + y = 0 1.
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