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
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
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?
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