first order differential equation



Mahery Raharinjatovo wrote:
> Hello
> How can I solve this ?quation with Maxima ?
> 'diff(x,t)^2+5*x^2=8
> ------------------------------------------------------------------------
>
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>   
The equation is not in a  standard form  that maxima expects. 

You can put it in the form by solving for (x')^2 and taking the square 
root.  You get two equations, each of which are separable and Maxima 
handles them just fine.
                               
(%i9) display2d: false;

(%o9) false
(%i10) solve('diff(x,t)^2 + 5*x^2=8,'diff(x,t));
/* of course you can do this by hand */
(%o10) ['diff(x,t,1) = -sqrt(8-5*x^2),'diff(x,t,1) = sqrt(8-5*x^2)]
(%i11) ode2(%o10[1],x,t);

(%o11) -asin(5*x/(2*sqrt(10)))/sqrt(5) = t+%c
(%i12) ode2(%o10[2],x,t);

(%o12) asin(5*x/(2*sqrt(10)))/sqrt(5) = t+%c

-sen