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(c) y(x) = A cos x + B sin x + x² (d) y(x) = A(x² − 1) + Bx

(c) y(x) = A cos x + B sin x + x² (d) y(x) = A(x² − 1) + Bx

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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Question

could you please help me with part c and d , please provide written out explanations 

2. Let A and B be arbitrary constants. For each of the following y(x), find a differential equation that y(x) satisfies, with the order of the ODE equal to the number of arbitrary constants in y(x). The ODE should not contain any arbitrary constants. (a) y(x) = cos x + Ax² (b) y(x) = sin(x + A) (c) y(x) = A cos x + B sin x + x² (d) y(x) = A(x² - 1) + Bx
Transcribed Image Text:2. Let A and B be arbitrary constants. For each of the following y(x), find a differential equation that y(x) satisfies, with the order of the ODE equal to the number of arbitrary constants in y(x). The ODE should not contain any arbitrary constants. (a) y(x) = cos x + Ax² (b) y(x) = sin(x + A) (c) y(x) = A cos x + B sin x + x² (d) y(x) = A(x² - 1) + Bx
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