Consider the differential equation y"-10y'+25y = 0. The characteristic equation is The solution(s) to the characteristic equation is/are r one unique solution, enter a comma separated list.) The general solution to the differential equation is 5x y = c₁e³x + c₂ïe5x -10x y = e -10x 25x + e y = c₁e +c₂e²5x -10x y = c₁e + c₂xе* y = e = e5x + xe5x y = c₁e5x + 25x . (Use the variable r.) 25x . (If there is more than

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 16E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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Question 3

Consider the differential equation y"-10y'+25y = 0.
The characteristic equation is
The solution(s) to the characteristic equation is/are r
one unique solution, enter a comma separated list.)
The general solution to the differential equation is
○y=c₁e5x + c₂xе5x
O
O
-10x
y = e te25x
-10x
y = c₁e
y = c₁e
-10x
+ c₂e²5x
+ c₂xе²
y =
= e5x
○ y = c₁e5ª + ²5x
хебх
. (Use the variable r.)
+ xe
25x
. (If there is more than
Transcribed Image Text:Consider the differential equation y"-10y'+25y = 0. The characteristic equation is The solution(s) to the characteristic equation is/are r one unique solution, enter a comma separated list.) The general solution to the differential equation is ○y=c₁e5x + c₂xе5x O O -10x y = e te25x -10x y = c₁e y = c₁e -10x + c₂e²5x + c₂xе² y = = e5x ○ y = c₁e5ª + ²5x хебх . (Use the variable r.) + xe 25x . (If there is more than
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Publisher:
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