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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
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

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 =
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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