initial value problem

[cazza90]

Solve the initial value problem (y^-2)dx - (e^x)/(e^2x +1) dy = 0, subject to the condition y(0) = 1.

All the examples that I look up for initial value problems have y prime somewhere in the equation, but never dy and dx. Am I supposed to some how separate y and dy from x and dx and then just integrate both sides?

 

[galactus]

y' is the same thing as dy/dx.

\(\displaystyle \frac{1}{y^{2}}dx=\frac{e^{x}}{e^{2x}+1}dy\)

Just separate your variables.

\(\displaystyle \frac{e^{2x}+1}{e^{x}}dx=y^{2}dy\)

Now, continue.