This question is an initial value problem for diffeq. We are asked to solve explicitly for y.(adsbygoogle = window.adsbygoogle || []).push({});

(1+cos(x))dy = ((e^(-y))+1)*sin(x)dx , y(0) = 0

I attempted a separation of variables and ended up with the following:

dy / ((e^(-y))+1) = (sin(x) / (1 + cos(x))) dx

I know that my next step is to integrate both sides and then solve using the given initial value, but I am unsure as to how I am supposed to integrate either side.

For the right side, I believe I can integrate using u-substitution, where:

u = cos(x) + 1

du / dx = -sin(x)

So that the right side becomes -1/u, integrates to -ln(u), then -ln(1+cos(x)).

For the left side, I've tried using partial fraction decomposition but end up either with my original equation or the natural logarithm of a negative number.

This is where I need help, is in the integration of the left hand side.

thank you

-twiztidmxcn

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# Homework Help: DiffEq - Initial Value Problem / Integration help

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