Question

d^3y/dx^3 -7 dy/dx-6y = e^2x (1+x)
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Answer 1

Answer:

d3y/dx3 − 3(d2y/dx2) + 4y = 0 The auxiliary equation is D3 − 3D2 + 4 = 0 Solving, the roots are −1, 2, 2. The root −1 gives the solution e−x . The double root 2 gives two solutions e2x , x e2x . The general solution is y = C1e−x + C2e2x + C3xe2xRead more on Sarthaks.com - https://www.sarthaks.com/442615/solve-d-3y-dx3-3-d-2y-dx-2-4y-0?show=442624#a442624