Solution Found!
Solved: In 37 through 40, use variation of parameters to
Chapter 4, Problem 39E(choose chapter or problem)
In Problems 37 through 40, use variation of parameters to find general solution to the differential equation given that the functions \(y_{1}\) and \(y_{2}\) are linearly independent solutions to the corresponding homogeneous equation for \(t>0). Remember to put the equation in standard form.
\(t y^{\prime \prime}+(5 t-1) y^{\prime}-5 y=t^{2} e^{-5 t}\) ;
\(y_{1}=5 t-1\) , \(y_{2}=e^{-5 t}\)
Equation Transcription:
Text Transcription:
y_{1}
y_{2}
t>0
t y’’+(5t-1)y’-5 y=t^{2} e^{-5t}
y_{1}=5 t-1
y_{2}=e^{-5t}
Questions & Answers
QUESTION:
In Problems 37 through 40, use variation of parameters to find general solution to the differential equation given that the functions \(y_{1}\) and \(y_{2}\) are linearly independent solutions to the corresponding homogeneous equation for \(t>0). Remember to put the equation in standard form.
\(t y^{\prime \prime}+(5 t-1) y^{\prime}-5 y=t^{2} e^{-5 t}\) ;
\(y_{1}=5 t-1\) , \(y_{2}=e^{-5 t}\)
Equation Transcription:
Text Transcription:
y_{1}
y_{2}
t>0
t y’’+(5t-1)y’-5 y=t^{2} e^{-5t}
y_{1}=5 t-1
y_{2}=e^{-5t}
ANSWER:
Solution
Step 1
In this question we need to find general solution of the given differential equation using variation of parameters method.
First let us write the given differential equation
in its standard form as :
y = te-5t …………………………………………………….(1)