MHB Converting a Second-Order IVP into a System of Equations: Can Substitution Help?

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The discussion focuses on converting a second-order initial value problem (IVP) into a system of first-order equations. The equation provided is y'' + y' - 2y = 0 with initial conditions y(0) = 2 and y'(0) = 0. By substituting u = y', the transformation leads to u' + u - 2y = 0, simplifying to u' = 2y - u. Participants express difficulty in managing the substitution process and seek guidance on the next steps in solving the system. The conversation emphasizes the importance of correctly applying substitutions to facilitate the solution of differential equations.
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Change the second-order IVP into a system of equations
$y''+y'-2y=0 \quad y(0)= 2\quad y'(0)=0$

let $u=y'$

ok I stuck on this substitution stuff
 
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Since y'= u, y''= u' so y''+ y'- 2y= u'+ u- 2y= 0 so u'= 2y-u.
 

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