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  • Find the general solution: x to the power 5 dy by dx equals minus y to the power 5

8. Find the general solution:

       x^5\frac{dy}{dx} = - y^5

Answers (1)

best_answer

Given, in the question

x^5\frac{dy}{dx} = - y^5

\\ \implies \int \frac{dy}{y^5} = - \int \frac{dx}{x^5} \\ \implies \frac{y^{-4}}{-4} = -\frac{x^{-4}}{-4} + C \\ \implies \frac{1}{y^4} + \frac{1}{x^4} = C

This is the required general equation.

Posted by

HARSH KANKARIA

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