Find the general solution of #dy/dx = 1/(ye^x)# ?

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Answer 1 · 2018-06-10T11:29:53

#:. y^2+2e^-x=k, or, (k-y^2)e^x=2#.

Rewriting the given Diff. Eqn. (DE) as,

#ydy=dx/e^x=e^-xdx#,

we immediately recognise it as a separable variable type.

To get its General Solution (GS) , we need to integrate it

term-wise.

#:. intydy=inte^-xdx+c#.

#:. y^2/2=-e^-x+c#.

#:. y^2+2e^-x=k, or, (k-y^2)e^x=2," where "(k=2c)#,

is the desired GS!