dy Use the substitution x = e to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for x²y" 3xy' + 13y = 2 + 3x X Solve the original equation by solving the new equation using the procedure in Sections 4.3-4.5. y(x) = x²(ccos (3 ln(x)) + cosin (3 ln(x))) Need Help? Read It 3x 2 ++ + 10 13. ,X>0 d²y dt² and ypp for.
dy Use the substitution x = e to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for x²y" 3xy' + 13y = 2 + 3x X Solve the original equation by solving the new equation using the procedure in Sections 4.3-4.5. y(x) = x²(ccos (3 ln(x)) + cosin (3 ln(x))) Need Help? Read It 3x 2 ++ + 10 13. ,X>0 d²y dt² and ypp for.
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:Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for
dt
x2y" 3xy' + 13y = 2 + 3x
X
Solve the original equation by solving the new equation using the procedure in Sections 4.3-4.5.
3x
y(x) = x²(c₁cos (3 ln(x)) + c₂sin( 3 ln(x) ) ) + ³0-
+
Need Help? Read It
2
13
, x > 0
and ypp for .)
d²y
dt²
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