Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation w d²y dy coefficients. (Use yp for and ypp dt dt² Ge&t + x²y" - 15xy' + 64y = 0 8x coxe X for ..) Solve the original equation by solving the new equation using the procedures in Sections 4.3-4.5.

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.CR: Chapter 11 Review
Problem 12CR
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4.7.9

Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation w
d²y
dt²
dy
coefficients. (Use yp for and ypp for
dt
8x
Ge&t
x²y" - 15xy' + 64y = 0
8x
Cate&x
coxe
+
Solve the original equation by solving the new equation using the procedures in Sections 4.3-4.5.
y(x) = €₁x³ + c₂ln(x)x8
..)
, x > 0
Transcribed Image Text:Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation w d²y dt² dy coefficients. (Use yp for and ypp for dt 8x Ge&t x²y" - 15xy' + 64y = 0 8x Cate&x coxe + Solve the original equation by solving the new equation using the procedures in Sections 4.3-4.5. y(x) = €₁x³ + c₂ln(x)x8 ..) , x > 0
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