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.

Understanding Business
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ISBN:9781259929434
Author:William Nickels
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Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
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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.
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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