Question

Form the differential equation corresponding to y² = m (a² – x²) by eliminating m and a.

Solution

The given equation is $straight y squared space equals space straight m left parenthesis straight a squared minus straight x squared right parenthesis$ ...(1)
Differentiating w.r.t.x, we get,
$2 straight y dy over dx space equals space straight m left parenthesis 0 minus 2 space straight x right parenthesis$
or $straight y dy over dx space equals space minus straight m space straight x$ ...(2)
Again differentiating w.r.t.x,
$straight y fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx. dy over dx space equals space minus straight m$
or $straight y space fraction numerator straight d squared straight y over denominator dx squared end fraction plus open parentheses dy over dx close parentheses squared space equals space minus open parentheses straight y fraction numerator begin display style dy over dx end style over denominator straight x end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space of space space left parenthesis 2 right parenthesis close square brackets$
or $xy fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x open parentheses dy over dx close parentheses squared space equals space straight y dy over dx$
Which is the required differential equation.

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Vector Algebra

Form the differential equation corresponding to y² = m (a² – x²) by eliminating m and a.

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Vector Algebra

Form the differential equation corresponding to y2 = m (a2 – x2) by eliminating m and a.

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Form the differential equation corresponding to y² = m (a² – x²) by eliminating m and a.