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Consider the differential equation y"= e ² + xy' where y is considered to be a function of x. In this exercise, you will determine whether or not x² 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 words, compute e ² + xy'. e² + xy = (c) Based on your answers to (a) and (b), can we say that y = e 2 is a solution to the differential equation? Yes O No

Consider the differential equation y"= e ² + xy' where y is considered to be a function of x. In this exercise, you will determine whether or not x² 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 words, compute e ² + xy'. e² + xy = (c) Based on your answers to (a) and (b), can we say that y = e 2 is a solution to the differential equation? Yes O 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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Consider the differential equation y"= e ² + xy' where y is considered to be a function of x. In this exercise, you will determine whether or not x² y = e 2 +cis 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 words, compute e ² + xy'. e² + xy= (c) Based on your answers to (a) and (b), can we say that y = e 2 is a solution to the differential equation? Yes O No
Transcribed Image Text:Consider the differential equation y"= e ² + xy' where y is considered to be a function of x. In this exercise, you will determine whether or not x² y = e 2 +cis 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 words, compute e ² + xy'. e² + xy= (c) Based on your answers to (a) and (b), can we say that y = e 2 is a solution to the differential equation? Yes O No
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