(a). t²y" - 4ty' +6y=0, t>0; y₁(t) = t² Assume that y2 = v(t)y₁, using above approach with p(t) = −4/t, we have t²v" + (4t4t)v' = 0 v" =0 v = c₁t + C₂ = (c₁t + c₂) t²
(a). t²y" - 4ty' +6y=0, t>0; y₁(t) = t² Assume that y2 = v(t)y₁, using above approach with p(t) = −4/t, we have t²v" + (4t4t)v' = 0 v" =0 v = c₁t + C₂ = (c₁t + c₂) t²
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
Section11.3: Euler's Method
Problem 1YT: Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.
Question
Can you explain how to get this answer step by step using redution of order
Transcribed Image Text:(a). t²y" - 4ty' +6y=0, t>0; y₁(t) = t²
Assume that y2 = v(t)y₁, using above approach with p(t) = −4/t, we have
t²v" + (4t4t)v' = 0
v" =0 v = c₁t + C₂
= (c₁t + c₂) t²
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