Obtain the Differential Equation by Eliminating Arbitrary Constants A, B from the Equation - Y = a Cos (Log X) + B Sin (Log X) - Mathematics and Statistics

Obtain the differential equation by eliminating arbitrary constants A, B from the equation -
y = A cos (log x) + B sin (log x)

Solution

y = Acos(logx)+Bsin(logx)

Diff. w.r.t x

dy/dx=-A(sin(logx))/x+B(cos(logx))/x

dy/dx=(-Asin(logx)+Bcos(logx))/x

x.dy/dx=-Asin(logx)+Bcos(logx)

Again diff. w.r.t. x

x.(d^2y)/(dx^2)+dy/dx=-A(cos(logx))/x-B(sin(logx))/x

x.(d^2y)/(dx^2)+dy/dx=-(Acos(logx)+Bsin(logx))/x

x.(d^2y)/(dx^2)+dy/dx=-y/x

x^2.(d^2y)/(dx^2)+x dy/dx+y=0

Concept: Formation of Differential Equation by Eliminating Arbitary Constant
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