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

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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.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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