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Vector Algebra

Question

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Solve $straight y apostrophe minus dy over dx space equals space minus straight x over straight y space left parenthesis straight y not equal to 0 right parenthesis.$

Solution

The given differential equation is

dy over dx equals negative straight x over straight y

Separation the variables, we get,

straight y space dy space equals space minus straight x space dx

Integrating,

integral straight y space dy space equals space minus integral straight x space dx

or

straight y squared over 2 space equals space minus straight x squared over 2 plus straight C subscript 1 space space space or space space straight x squared plus straight y squared space equals straight c

is required solution.

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