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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The general solution of the differential equation
$(D^2 - a^2)^3 y = e^{ax}$, where $D=\frac{d}{dx}$ is
Solution
Characteristic equation:
$(m^2-a^2)^3=0$
Roots: $m=\pm a$ each of multiplicity 3.
Hence complementary function:
$(c_1+c_2x+c_3x^2)e^{ax}+(c_4+c_5x+c_6x^2)e^{-ax}$
Since RHS is $e^{ax}$ and $m=a$ has multiplicity 3,
Particular integral = $x^3\frac{e^{ax}}{3!\,(2a)^3} =\frac{x^2e^{ax}}{8a^2}$
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