Form the differential equation of the family of curves given by y=Ae^mx+Be^-mx
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defferentiate w.r.t x
dy/dx=mAe^mx-mBe^-mx----------(1)
again defferentiate w.r.t x
d2y/dx2=m^2Ae^mx+m^2Be^-mx
= m^2 (Ae^mx+Be^-mx)
=m^2 .y ( given into question)
so, differencial equation
d2y/dx2=m^2y
dy/dx=mAe^mx-mBe^-mx----------(1)
again defferentiate w.r.t x
d2y/dx2=m^2Ae^mx+m^2Be^-mx
= m^2 (Ae^mx+Be^-mx)
=m^2 .y ( given into question)
so, differencial equation
d2y/dx2=m^2y
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