- #1
Kawakaze
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- 0
Homework Statement
Which of the methods of finding analytic solutions of differential equations
could you use to solve this equation? Give reasons for
your answer.
a
[tex]y+\frac{dy}{dx}tan(x) = 2 (\pi/4 \leq x < \pi/2)[/tex]
b
[tex]\sqrt{t^2+9}\frac{dy}{dx}=y^2 (0<y)[/tex]
The Attempt at a Solution
The integrating factor method for both, the initial value part I don't have a problem with,
For part a, I hit a wall when it came to integrating for the solution
I got g(x)=1, and h(x)=2/tan(x)
the integrating factor I got as p(x)=exp(x)
Putting it all back together I came unstuck here
[tex]exp(x)y=\int{exp(x)2cot(x)} dx[/tex]
Mainly because to get the same answer as wolphram alpha, I had to use the exp funion on the RHS to get rid of the LN that came from integrating the cotangent. Meaning then that I can't eliminate the exp from the LHS. So I am confused and haven't attempted part b yet, but I think it is also to be solved in the same way.