4. (9 points). Functions y₁ and y₂ are solutions for the corresponding homogeneous equation of the following differential equation. ty" - (1+t)y' + y = t²e²t, t>0; y₁ = 1+t, y₂ = et. a) Use the Variation Method to find a particular solution of the equation. b) Write the General solution of the equation. c) Determine the solution for the differential equation that satisfies initial values y(1) 0 and y' (1) = 4.
4. (9 points). Functions y₁ and y₂ are solutions for the corresponding homogeneous equation of the following differential equation. ty" - (1+t)y' + y = t²e²t, t>0; y₁ = 1+t, y₂ = et. a) Use the Variation Method to find a particular solution of the equation. b) Write the General solution of the equation. c) Determine the solution for the differential equation that satisfies initial values y(1) 0 and y' (1) = 4.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.5: Shortest Path Models
Problem 30P
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Transcribed Image Text:4. (9 points). Functions y₁ and y₂ are solutions for the corresponding homogeneous equation of
the following differential equation.
ty" - (1+t)y' + y = t²e²t, t>0; y₁ = 1+t, y₂ = et.
a) Use the Variation Method to find a particular solution of the equation.
b) Write the General solution of the equation.
c) Determine the solution for the differential equation that satisfies initial values
y(1) 0 and y' (1) = 4.
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