2. Prove that the functions in the right-hand column below are solutions of the differential equations in the left-hand columns. (Be sure to state the common interval for which solution and differential equation make sense.) (a) y' + y = 0 (b) y' = e 1 √1-x² f"(x) (c) dx2 (d) f'(x) (e) xy' (f) (1+x²)y dr (α) 008 A 2y = xy 2r sin A - 0 y = e-*. y = e*. y = x Arc sinx+√1-x². y = e² + 2. x². y = y = √1+x². a sec² A
2. Prove that the functions in the right-hand column below are solutions of the differential equations in the left-hand columns. (Be sure to state the common interval for which solution and differential equation make sense.) (a) y' + y = 0 (b) y' = e 1 √1-x² f"(x) (c) dx2 (d) f'(x) (e) xy' (f) (1+x²)y dr (α) 008 A 2y = xy 2r sin A - 0 y = e-*. y = e*. y = x Arc sinx+√1-x². y = e² + 2. x². y = y = √1+x². a sec² A
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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i need help with f,g, and i with an explanation. please, thank you
Transcribed Image Text:2. Prove that the functions in the right-hand column below are solutions of the
differential equations in the left-hand columns. (Be sure to state the common
interval for which solution and differential equation make sense.)
(a) y' + y = 0
(b) y' = e
(c)
d²y
dx2
/1
(d) f'(x) = f'(x)
2y
(e) xy'
(f) (1 + x²³)y' = xy
dr
do
(g) cos 0
(h) y"
(i) f'(x)
1
-
2r sin 0 = 0
· y = 0
=
f(x)
x2
(i) xy + y =
= y²
(k) x + yy' = 0
y = e-*.
y = e.
y = x Arc sinx+√1-x².
y = e² + 2.
y =
x².
T =
√1+x².
a sec² 0.
y = ae* + be *.
f(x) = 2e²/3.
2
x + 2
y =√16x².
y =
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