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Homework 5 Solutions

# How do i do this secondorder differential equations

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Unformatted text preview: λ3 = 4 −2/3 K ρc 4π G 1/ 2 = 6.7 × 1010 f (β ) πG 1/ 2 ρ−1/3 c so M= −4πρc ρ−1 c 6.7 × 1010 f (β ) πG 3/ 2 2 ξ1 dD dξ ξ1 = 1.4 × 10 = 70 32 1−β β4 1−β β4 1/ 2 kg × 1M 1.99 × 1030 kg 1/ 2 M β M (Msun) 0.1 6640 0.5 200 0.9 82 These are really large masses! This mainly goes to show how unimportant radiation pressure is inside stars like the Sun. NOTE ON SOLUTION: You may not use Mathematica/Matlab “differential solve” (e.g., DSolve, NDSolve) functions to do this – you need to do the integration on your own (it’s good for the soul!). You can either write a simple code in any language, or it’s even possible to do this in an Excel/OpenOffice spreadsheet. In any case, you must show and describe your own work. HOW DO I DO THIS? Second ­order differential equations can be integrated using the Euler method by solving two equations: one for the parameter and one for its derivative. In this case, the Lane ­Emden equation can be written as: d2 D 2 dD + = −Dn 2 dξ ξ dξ which can be split into two first ­ord...
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