Question

solve diff equation

dy/dx =(sec^2(y))/(1+x^2)

Answer 1

\[\frac{dy}{dx} = \frac{\sec^2 y}{1 + x^2}\]
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?

Answer 2

yes. the Integration is the problem i'm having trouble with

Answer 3

okay first turn dy/ sec^2 y into cos^2 y dy

you agree those are the same right?

Answer 4

\[\implies \int \cos^2 y dy = \int \frac{dx}{1+x^2}\]

Answer 5

yes now i see.

Answer 6

wonderful

Answer 7

thanks

Answer 8

welcome

Answer 9

what about 1/(1+x^2)

Answer 10

trigonometric substitution

Answer 11

is it tan?

Answer 12

arctan*

Answer 13

right

Answer 14

yes

Answer 15

that's what I thought. Thanks

Answer 16

welcome