TS EAMCET 20-July-2022 Shift 2 Solved Paper

Given that y=ax2+b‌log‌x
⇒‌‌‌

y

x2

=a+b‌log‌x
On differentiating w.r.t. x,
‌‌

1

x2

y′−‌

2

x3

y=‌

b

x

⇒‌‌‌

1

x

y′−‌

2

x2

y=b
Again differentiating w.r.t. x,
‌‌

1

x

y′′−‌

y′

x2

+‌

4y

x3

⋅‌

2

x2

y′=0
⇒−‌

1

x

y′′+‌

3y′

x2

=‌

4y

x3

⇒−xy′′+3y′=‌

4y

x

On comparing with
f(x)y′′+g(x)y′=‌

4y

x

∴‌‌f(x)=−x, and g(x)=3
an m=1 degree of differential equation
∴‌‌f(l)+g(l)=−1+3=2
Order of differential equation i.e. f(m)+g(m)=l