Given an IVP Fundamental Existence Theorem for Linear Differential Equations +1() +a()+ao()uo(x) (0) - M-1 v(ro). (ro) If the coefficients a, (),...,ao(a) and the right hand side of the equation p(e) are continuous on an interval I and if a, (a) 0 on I then the IVP has a unique solution for the point o I that exists on the whole interval I. Consider the IVP on the whole real line d₂"-1 dz +...+ d'y dz³ 1 dy ²+-9 dz +y=sin(x) (-1)-55, (-1)-12, "(-1)-8, "(-1)-2, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval
Given an IVP Fundamental Existence Theorem for Linear Differential Equations +1() +a()+ao()uo(x) (0) - M-1 v(ro). (ro) If the coefficients a, (),...,ao(a) and the right hand side of the equation p(e) are continuous on an interval I and if a, (a) 0 on I then the IVP has a unique solution for the point o I that exists on the whole interval I. Consider the IVP on the whole real line d₂"-1 dz +...+ d'y dz³ 1 dy ²+-9 dz +y=sin(x) (-1)-55, (-1)-12, "(-1)-8, "(-1)-2, The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval
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:HW06-3.2: Problem 2
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Given an IVP
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Fundamental Existence Theorem for Linear Differential Equations
+ a(z)
v(zo) . (ro)-3₁₁-¹)(20) - M-1
If the coefficients a, (2),..., ao() and the right hand side of the equation g(e) are continuous on an interval I and if a, (a) 0 on I then the IVP has a unique
solution for the point o I that exists on the whole interval I.
Consider the IVP on the whole real line
d'y
dz³
-y=sin(z)
"(-1)=2,
(-1)-55, (-1) = 12, "(-1)-8,
The Fundamental Existence Theorem for Linear Differential Equations guarantees the existence of a unique solution on the interval
(22 - 9)
+...+ a(z) + a(z)v-g(x)
dz
dz
1 dy
z²+9 dz
+
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