Question

y=x^2-2x+5 show that 4(d^2y/dx^2)+(x-1)dy/dX=2y​

Answer 1

Step-by-step explanation:

y= x^2-2x+5

differentiating w r t x

dy/dx = 2x-2............(1)

differentiating w r r x

d2y/dx^2= 2............(2)

consider

4(d2y/dx^2)+(x-1) dy/DX

= 4(2)+(x-1)(2x-2)

= 8+2x^2-2x-2x+2

=2x^2-4x+10

=2(x^2-2x+5)

=2y

: hence it is proved