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The second-order differential equation in an unknown function u: u(x,y) is defined as ∂²u/∂x² = 2. Assuming g: g(x), f: f(y), and h: h(y), the general solution of the above differential equation is

1. u = x² + f(y) + g(x)
2. u = x² + x f(y) + h(y)
3. u = x² + x f(y) + g(x)
4. u = x² + f(y) + y g(x)

Correct answer: u = x² + x f(y) + h(y)

Solution

Integrating d2u/dx2 = 2 twice with respect to x gives u = x^2 + x*f(y) + h(y), where the two integration 'constants' are arbitrary functions of y. This is option idx 1; the stored idx 3 with y*g(x) is incorrect.

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