Question

Why e^In y=e^2x^2+c become y=e^2x^2*e^c?

Answer 1

it looks like what you had was
\[ln(y) = 2x^2+c\]
and then to solve for y, we raise both sides as a power of e
\[e^{ln(y)}=e^{2x^2+c}\]
now on the right had side we use the property that
\[a^{b+c}=a^b*a^c\]
and on the left hand side we use the fact that
\[e^{ln(y)}=y\]putting those both together we have
\[y=e^{2x^2+c}=e^{2x^2}*e^c\]
does this make sense?

Answer 2

so\[e^{ln(y)}=e^{2x^2+c}\iff y=e^{2x^2}e^c\]

Answer 3

Okay, I got it. Thanks zzrock3r. :)