GATE CE 1994 | Differential Equations Question 50 | Engineering Mathematics

GATE CE 1994

MCQ (Single Correct Answer)

-0.3

The necessary & sufficient condition for the differential equation of the form $$\,\,M\left( {x,y} \right)dx + N\left( {x,y} \right)dy = 0\,\,$$ to be exact is

$$M=N$$

$${{\partial M} \over {\partial x}} = {{\partial N} \over {\partial y}}$$

$${{\partial M} \over {\partial y}} = {{\partial N} \over {\partial x}}$$

$${{{\partial ^2}M} \over {\partial {x^2}}} = {{{\partial ^2}N} \over {\partial {y^2}}}$$

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