# Solving and plotting this differential equation

• Jan 27th 2013, 05:48 AM
intermilan631848
Solving and plotting this differential equation
Hi i have the differential equations:

$\frac{1}{M_{\phi}} \frac{d (p_{\phi}(a) a^3)}{d a} = -\sqrt{\frac{3}{8}} \frac{a}{\sqrt{p_{\phi}(a) a^{4}M_{\phi}+p_{R}(a)a^4}}$

$\frac{1}{M_{\phi}^{2}} \frac{d (p_{R}(a) a^4)}{d a} = \sqrt{\frac{3}{8}} \frac{a^2}{\sqrt{p_{\phi}(a) a^{4}M_{\phi}+p_{R}(a)a^4}} + \sqrt{2}\frac{a^{-1}}{\sqrt{p_{\phi}(a) a^{4}M_{\phi}}} [(p_{x}(a)a^3)^2 - (2\pi)^{\frac{2}{3}}a^3 T^{\frac{3}{2}e^{\frac{-M_{\phi}}{T}}]$
$\frac{d (p_{x}(a) a^3)}{d a} = -\sqrt{2}\frac{a^{-2}}{\sqrt{p_{\phi}(a) a^{4}M_{\phi}}} [(p_{x}(a)a^3)^2 - (2\pi)^{\frac{2}{3}}a^3 T^{\frac{3}{2}e^{\frac{-M_{\phi}}{T}}]$

and want to solve them and plot them subject to the initial conditions, $a=a_{I}, p_{\phi}(a)= p_{\phi I} , p_{R}(a_{I})=p_{x}(a)=0$ and find T from the graph ( $M_{\phi}=10^{10}$)

I think the easiest way is with maple but am open to suggestions, basically i am struggling with maple to actually solve these equations to give express for $p_{\phi}, p_{R},p_{x}$.
Any help would be appreciated