Answer:
[tex]\frac{ d^{2} y}{dx^{2} } = -10[/tex]
Step-by-step explanation:
Concept : We have to differentiate the given equation twice and then put the values of x and y at the given point.
The given point is (2,-5).
Given xy - y = -5
Differentiating both sides,
[tex] x \times \frac{dy}{dx} + y - \frac{dy}{dx}[/tex] = 0
Substitute (x,y) as (2,-5)
[tex]2 \times \frac{dy}{dx} -5 - \frac{dy}{dx}[/tex] = 0
[tex]\frac{dy}{dx} = 5[/tex]
Differentiating again, we get
[tex]\frac{dy}{dx} + x \times \frac{ d^{2} y}{dx^{2} } + \frac{dy}{dx} - \frac{ d^{2} y}{dx^{2} } = 0[/tex]
Substitute values of x , y and \frac{dy}{dx} ,
[tex]5 + 2 \times \frac{ d^{2} y}{dx^{2} } + 5 - \frac{ d^{2} y}{dx^{2} } = 0[/tex]
[tex]\frac{ d^{2} y}{dx^{2} } = -10[/tex]
