Problem with differential equation (DESOLVE)

[ZellAllon]

Hello,

I don't know why when I try to solve a Homogeneous differential equation my hp prime I get something like:

desolve((y') = ((y/x)+(x/y)),y) = [pnt[G_0*e^((1/2)*_(t38)^2),G_0*_(t38)*e^((1/2)*_(t38)^2)]]

the solution must be Y^2=X^2*LN(X^2)+C*X^2

anyone can help me? please.

[salvomic]

(03-03-2015 05:29 PM)ZellAllon Wrote:  Hello,

I don't know why when I try to solve a Homogeneous differential equation my hp prime I get something like:

desolve((y') = ((y/x)+(x/y)),y) = [pnt[G_0*e^((1/2)*_(t38)^2),G_0*_(t38)*e^((1/2)*_(t38)^2)]]

the solution must be Y^2=X^2*LN(X^2)+C*X^2

anyone can help me? please.

see here: Parisse replied to me few time ago...


the "strange" expression should be like
\[ y=c*e^{\frac{t^{2}}{2}} \ AND \ y=c*t*e^{\frac{t^{2}}{2}} \]

G_0 ok for "c", but, yes, "_t38" is a bit bizzarre, and we are lucky that it is not "p38"

Note also that \( e^{\frac{t^{2}}{2}} \) is simply \( \sqrt{e^{t^{2}}} \) ...

[parisse]

You get parametric solutions currently. With Xcas current CAS version, you would get
[√2*x*√(ln(x/G_0)),-√2*x*√(ln(x/G_0))]

[ZellAllon]

(03-03-2015 06:59 PM)salvomic Wrote:  

(03-03-2015 05:29 PM)ZellAllon Wrote:  Hello,

I don't know why when I try to solve a Homogeneous differential equation my hp prime I get something like:

desolve((y') = ((y/x)+(x/y)),y) = [pnt[G_0*e^((1/2)*_(t38)^2),G_0*_(t38)*e^((1/2)*_(t38)^2)]]

the solution must be Y^2=X^2*LN(X^2)+C*X^2

anyone can help me? please.

see here: Parisse replied to me few time ago...


the "strange" expression should be like
\[ y=c*e^{\frac{t^{2}}{2}} \ AND \ y=c*t*e^{\frac{t^{2}}{2}} \]

G_0 ok for "c", but, yes, "_t38" is a bit bizzarre, and we are lucky that it is not "p38"

Note also that \( e^{\frac{t^{2}}{2}} \) is simply \( \sqrt{e^{t^{2}}} \) ...

ok, understood, thanks.But how can I take these parametric solutions and get y as a function of x?

[ZellAllon]

(03-04-2015 10:07 AM)parisse Wrote:  You get parametric solutions currently. With Xcas current CAS version, you would get
[√2*x*√(ln(x/G_0)),-√2*x*√(ln(x/G_0))]

Hello,

How do you get that solution? explain to me please!

[Tim Wessman]

(03-04-2015 05:44 PM)ZellAllon Wrote:  How do you get that solution? explain to me please!

That is the author of the CAS inside Prime. He is using the pc version (which is newer then the current version in Prime) and that result is returned. If/Until that code is put into the Prime firmware the calculator will continue to return the result you posted.