Q. 305.0( 2 Votes )

If y = 3 cos (log

Answer :

Note: y2 represents second order derivative i.e. and y1 = dy/dx


Given,


y = 3 cos (log x) + 4 sin (log x) ……equation 1


to prove: x2y2+xy1+ y =0


We notice a second order derivative in the expression to be proved so first take the step to find the second order derivative.


Let’s find


As,


So, lets first find dy/dx



Let, log x = t


y = 3cos t + 4sin t …………….equation 2



………….equation 3



……...equation 4


Again differentiating w.r.t x:


Using product rule of differentiation we have




Using equation 2,3 and 4 we can substitute above equation as:




Multiplying x2 both sides:



x2y2+xy1+ y =0 ………..proved

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