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anonymous
 3 years ago
solve diff equation
dy/dx =(sec^2(y))/(1+x^2)
anonymous
 3 years ago
solve diff equation dy/dx =(sec^2(y))/(1+x^2)

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{dy}{dx} = \frac{\sec^2 y}{1 + x^2}\] divide both sides by sec^2 y \[\implies \frac{dy}{\sec^2 y dx} = \frac{1}{1+x^2}\] now multiply both sides by dx \[\implies \frac{dy}{\sec^2 y} = \frac{dx}{1+x^2}\] now you can integrate both sides \[\implies \int \frac{dy}{\sec^2 y} = \int \frac{dx}{1+x^2}\] does that help?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes. the Integration is the problem i'm having trouble with

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0okay first turn dy/ sec^2 y into cos^2 y dy you agree those are the same right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\implies \int \cos^2 y dy = \int \frac{dx}{1+x^2}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0trigonometric substitution

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that's what I thought. Thanks
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