Yefim S. answered • 19d

Math Tutor with Experience

SEparate variables: (e^{y} + ye^{y})dy = - e^{x}dx;

We integrate now both sides: ∫(e^{y} + ye^{y})dy = - ∫e^{x}dx; e^{y} + ye^{y} - e^{y } = - e^{x} + C; ye^{y} = - e^{x} + C.

y(0) = 0; 0·e^{0} = - 1 + C; C = 0.

So, ye^{y} = - e^{x} + 1 is implicit solution of this IVP

Adam B.

19d

Mel L.

and with y(0) = −1 is it an implicit solution too?19d