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Find the particular solution of the diff...

Find the particular solution of the differential equation `(1 + e^(2x)) dy + (1 + y^2) e^x dx = 0`, given that `y = 1 w h e n x = 0`.

Text Solution

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Given differential equation is `(1 + e^(2x))dy + (1 + y^2)e^xdx = 0`
Above equation may be written as On integrating both sides,
we get On putting `e^x = t` or `e^x dx = dt` in RHS,
we get Also, given that y = 1, when x = 0.
On putting above values in Eq. (i), we get On putting C =
`pi/2` in Eq. (i), we get which is the required solution
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