Find the fundamental set of solutions of the following equations and discuss their long term behaviors. No need to check Wronskian. (a) y" + y' − 6y = 0 (b) y" +2y' + 5y = 0 (c) y″ – 8y' + 16y = 0
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- In this problem we outline a different derivation of Euler's formula. Show (formally) that y = eit is also a solution of y″ + y = 0. Therefore, (31) eit=c1cost+c2sint for some constants c1 and c2. Why is this so?3. Find the complementary solution of the equation y" - 5y" +7y' – 3y = 02. Find the general solution of the first-order equation dy_ y? – 2ry dr
- C. Eliminate the arbitrary constants in each equation and express the final answers in the following form: a,n(x)y(n) + an-1(x)yn-1) + . .. + a1(x)y' + ao(x)y – g(x) = 0 . 1. r* – y² = cy 2. y = cje" + cze²" + c3e*rFind a particular solution to y″+36y = 60sin(6t).Find two solutions to 2y′′+ 5y′+ 2y= 0.