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Engineering Mathematics Question on Single and multi-step methods for first order differential equations

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

A

u=x2+f(y)+g(x)u=x^2+f(y)+g(x)

B

u=x2+xf(y)+h(x)u=x^2+xf(y)+h(x)

C

u=x2+xf(y)+g(x)u=x^2+xf(y)+g(x)

D

u=x2+f(y)+yg(x)u=x^2+f(y)+yg(x)

Answer

u=x2+xf(y)+h(x)u=x^2+xf(y)+h(x)

Explanation

Solution

The correct option is (B) :u=x2+xf(y)+h(x)u=x^2+xf(y)+h(x)