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Consider the differential equation y" = e ²² + xy where y is considered to be a function of . In this exercise, you will determine whether or not ,2 y = e 2 + c is a solution to the differential equation for any constant c. (a) First substitute the above expression for y into the left side of the differential equation. In other words, compute y". y": (b) Next substitute the above expression for Y into the right side of the differential equation. In other 2.2 words, compute e + xy'. 2 z2 e² + xy = (c) Based on your answers to (a) and (b), can we say 2:2 that ye is a solution to the differential equation? Yes No

Consider the differential equation y" = e ²² + xy where y is considered to be a function of . In this exercise, you will determine whether or not ,2 y = e 2 + c is a solution to the differential equation for any constant c. (a) First substitute the above expression for y into the left side of the differential equation. In other words, compute y". y": (b) Next substitute the above expression for Y into the right side of the differential equation. In other 2.2 words, compute e + xy'. 2 z2 e² + xy = (c) Based on your answers to (a) and (b), can we say 2:2 that ye is a solution to the differential equation? Yes No

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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4:19 Done Consider the differential equation y'= e ² + xy y" ✰ myopenmath.com where y is considered to be a function of x. In this exercise, you will determine whether or not z2 y = e 2 + c is a solution to the differential equation for any constant c. (a) First substitute the above expression for y into the left side of the differential equation. In other words, compute y". e²² + xy = е (b) Next substitute the above expression for y into the right side of the differential equation. In other 22 words, compute e 2 + xy. Yes No .5G 50 Question Help: AA (c) Based on your answers to (a) and (b), can we say 22 that y = e 2 is a solution to the differential equation? Video ✩
Transcribed Image Text:4:19 Done Consider the differential equation y'= e ² + xy y" ✰ myopenmath.com where y is considered to be a function of x. In this exercise, you will determine whether or not z2 y = e 2 + c is a solution to the differential equation for any constant c. (a) First substitute the above expression for y into the left side of the differential equation. In other words, compute y". e²² + xy = е (b) Next substitute the above expression for y into the right side of the differential equation. In other 22 words, compute e 2 + xy. Yes No .5G 50 Question Help: AA (c) Based on your answers to (a) and (b), can we say 22 that y = e 2 is a solution to the differential equation? Video ✩
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