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ANTONII [103]
3 years ago
14

Consider the differential equation: dy/dx = (y-2)(x^2+1)

Mathematics
1 answer:
Klio2033 [76]3 years ago
3 0

Answer:

6

Step-by-step explanation:

Given,

\dfrac{dy}{dx}=(y-2)(x^2+1) ...(i)

Differentiating w.r. to x.

\dfrac{d^2y}{dx^2}= (y-2)(2x)+ (x^2+1)\dfrac{dy}{dx}

From equation (1)

\dfrac{d^2y}{dx^2}= (y-2)(2x)+ (x^2+1)^2(y-2)

Now, at the point (1,3)

\dfrac{d^2y}{dx^2}= (3-2)(2\times 1)+ (1^2+1)^2(3-2)

\dfrac{d^2y}{dx^2}=6

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