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Vector Algebra

Question

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Solve:
$dy over dx equals straight e to the power of straight x minus straight y end exponent plus straight x squared straight e to the power of straight y$

Solution

dy over dx equals straight e to the power of straight x minus straight y end exponent plus straight x squared straight e to the power of straight x space space space space rightwards double arrow space space space space dy over dx space equals space straight e to the power of straight x. space straight e to the power of straight y plus space straight x squared. space straight e to the power of straight y.

rightwards double arrow space space space space space space space dy over dx space equals space left parenthesis straight e to the power of straight x plus straight x squared right parenthesis space straight e to the power of straight y

Separating the variables, we get,

dy over straight e to the power of negative straight y end exponent space equals space left parenthesis straight e to the power of straight x plus straight x squared right parenthesis dx space space rightwards double arrow space space space integral straight e to the power of straight y space dy space space equals space integral left parenthesis straight e to the power of straight x plus straight x squared right parenthesis space dx

therefore space space space space straight e to the power of straight y space equals space straight e to the power of straight x plus straight x cubed over 3 plus straight c

which is the required solution.

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