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Solving IVP: y' + p(t)y = g(t), y(to) = Yo Step 1: Construct the integrating factor u(t) = eJ p(t) dt . Step 2: Multiply D.E.by µ(t): Step 3: Rewrite D.E.:(µ(t) · y)' = µ(t) · g(t) Step 4: Integrate both sides: µ(t) · y = S µ(t) · g(t) dt: Step 5: Solve for y: Step 6: Impose Initial Condition y(to) = Yo to determine C:

Solving IVP: y' + p(t)y = g(t), y(to) = Yo Step 1: Construct the integrating factor u(t) = eJ p(t) dt . Step 2: Multiply D.E.by µ(t): Step 3: Rewrite D.E.:(µ(t) · y)' = µ(t) · g(t) Step 4: Integrate both sides: µ(t) · y = S µ(t) · g(t) dt: Step 5: Solve for y: Step 6: Impose Initial Condition y(to) = Yo to determine C:

Advanced Engineering Mathematics
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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Solving IVP: y' + p(t)y = g(t), y(to) = Y0 Step 1: Construct the integrating factor u(t) = eJ p(t) di. Step 2: Multiply D.E.by µ(t): Step 3: Rewrite D.E.:(u(t) - y)' = µ(t) - g(t) Step 4: Integrate both sides: µ(t) · y = S µ(t) · g(t) dt: Step 5: Solve for y: Step 6: Impose Initial Condition y(to) = Yo to determine C:
Transcribed Image Text:Solving IVP: y' + p(t)y = g(t), y(to) = Y0 Step 1: Construct the integrating factor u(t) = eJ p(t) di. Step 2: Multiply D.E.by µ(t): Step 3: Rewrite D.E.:(u(t) - y)' = µ(t) - g(t) Step 4: Integrate both sides: µ(t) · y = S µ(t) · g(t) dt: Step 5: Solve for y: Step 6: Impose Initial Condition y(to) = Yo to determine C:
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