solution of this differential equations
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y = ae^2x + be^-x
diff. w.r.t. x
dy/dx=2ae^2x - be^-x
again, diff w.r.t. x
d2y/dx2 = 4ae^2x + be^-x
d2y/dx2 = (2ae^2x - be^-x) + 2ae^2x +2be^-x
d2y/dx2 = dy/dx+ 2(ae^2x +be^-x)
d2y/dx2 = dy/dx+ 2y
d2y/dx2 - dy/dx - 2y = 0
diff. w.r.t. x
dy/dx=2ae^2x - be^-x
again, diff w.r.t. x
d2y/dx2 = 4ae^2x + be^-x
d2y/dx2 = (2ae^2x - be^-x) + 2ae^2x +2be^-x
d2y/dx2 = dy/dx+ 2(ae^2x +be^-x)
d2y/dx2 = dy/dx+ 2y
d2y/dx2 - dy/dx - 2y = 0
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