Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d²y dx² When y = dy dx d²y dx² = = Cyxe3x, (3c₁ + €₂) e³r x + 3x-c₂e³x 3r dy +9y=0; y = c₁e³x + dx ₁₂e³x + 9c₁e³x + ³c₂e³x + 3c₂e³+ + 9c₂re ³x Thus, in terms of x, d²y dy dx² dx 8 Ste3t + 9y = +9(c_e3X + C,xe3x)
Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d²y dx² When y = dy dx d²y dx² = = Cyxe3x, (3c₁ + €₂) e³r x + 3x-c₂e³x 3r dy +9y=0; y = c₁e³x + dx ₁₂e³x + 9c₁e³x + ³c₂e³x + 3c₂e³+ + 9c₂re ³x Thus, in terms of x, d²y dy dx² dx 8 Ste3t + 9y = +9(c_e3X + C,xe3x)
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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Transcribed Image Text:Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
d²y
dx²
dy
dx
d²y
dx²
When y = c₁e³x + ₂xe³x,
C
dy
dx
6-
dx
3x
+ 9y = 0; y = c₁e³x + ₂x³x
(3c₁ + €₂) e ³x + 3x
3x
9c₁e³x
Thus, in terms of x,
d²y
+9y =
dx²
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+ 3x-c₂e³x
+3c₂e³x + 3c2e³x +
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3x
9c₂xe ³x
+ 9(ce3X + C,xe3x)
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