Consider the initial value problem below where b denotes a given constant. Find the solution as a function of b and then determine the critical value of b that separates solutions that grow positively from those that eventually grow negatively. y′′ −y′ +0.25y=0,      y(0)=2,         y′(0)=b,

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.