Question

The differential equation whose solution is Ax² + By² = 1, where A and B are arbitrary constants is of

second order and second degree

first order and second degree

first order and first degree

second order and first degree

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Solution

second order and first degree

Ax squared space plus By squared space equals space 1 space space space space..... space left parenthesis 1 right parenthesis Ax space plus space By dy over dx space equals 0 space.... space left parenthesis 2 right parenthesis straight A space plus By space fraction numerator straight d squared straight y over denominator dx squared end fraction space plus straight B open parentheses dy over dx close parentheses squared space equals 0 space.... space left parenthesis 3 space right parenthesis straight x open curly brackets negative By fraction numerator straight d squared straight y over denominator dx squared end fraction minus straight B open parentheses dy over dx close parentheses squared close curly brackets plus By dy over dx space equals space 0 rightwards double arrow xy fraction numerator straight d squared straight y over denominator dx squared end fraction space plus straight x space open parentheses dy over dx close parentheses squared minus straight y dy over dx space equals space 0

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