       Re: Finding solutions to differential eqns

• To: mathgroup at smc.vnet.net
• Subject: [mg40111] Re: Finding solutions to differential eqns
• From: bobhanlon at aol.com (Bob Hanlon)
• Date: Fri, 21 Mar 2003 02:36:27 -0500 (EST)
• References: <b5bjbn\$5qp\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```eqn = 2*x[t]*t*(1+t)*x'[t]==1+x[t]^2;

soln = DSolve[eqn, x[t], t]//Flatten // Simplify

eqn /. ({#, D[#,t]}& /@ soln) // Simplify

eqn = x'[t] == (t/x[t])*Exp[-x[t]/t]+x[t]/t

soln = DSolve[eqn, x[t], t] // Flatten

eqn /. ({#, D[#,t]}& /@ soln) // Simplify

eqn = x'[t] == (t-4)*Exp[4*t]+t*x[t];

soln = DSolve[eqn, x[t], t]//Flatten // Simplify

eqn /. ({#, D[#,t]}& /@ soln) // Simplify

Bob Hanlon

In article <b5bjbn\$5qp\$1 at smc.vnet.net>, davidol at hushmail.com (David) wrote:

<<
Subject:	Finding solutions to differential eqns
From:		davidol at hushmail.com (David)
To: mathgroup at smc.vnet.net
Date:		Thu, 20 Mar 2003 05:25:11 +0000 (UTC)

Is there a method where you can get Mathematica to find general
solutions for differential equations?  For example:

[2xt(1 + t)]dx/dt = 1 + x^2

dx/dt = (t/x)e^(-x/t) + x/t

and

dx/dt = (t - 4)e^4t + tx

Cheers,

David

>><BR><BR>

```

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