# [Maxima] Problems with ode2 - integral known to maixma is not evaluated

Robert Marik marik at mendelu.cz
Sat May 2 19:21:58 CDT 2009

```Dear members of gmane.comp.mathematics.maxima.general and Maxima developers

if I try to solve the following linear second order ODE, the answer includes
unevaluated integral of x*%e^x*sin(x), even though maxima can evaluate this
integral. Using ev(%,nouns) evaluates this integral, but I think that it should
be evaluated immediately by ode2. Is something missing in definition of ode2?

Thank you
Robert Marik

Maxima 5.18.0 http://maxima.sourceforge.net
Using Lisp CMU Common Lisp CVS 19d 19d-release (19D)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) display2d:false;

(%o1) false
(%i2)  ode2('diff(y,x,2)+2*'diff(y,x)+1*y=x^2-sin(x)-cos(x)-exp(x)*sin(x),y,x);

(%o2) y = %e^-x*(50*'integrate(x*%e^x*sin(x),x)
+((-25*x-25)*%e^x-6*%e^(2*x))*sin(x)
+(8*%e^(2*x)+25*x*%e^x)*cos(x)+(50*x^2-200*x+300)*%e^x)
/50
+(%k2*x+%k1)*%e^-x
(%i3) ev(%,nouns);

(%o3) y = %e^-x*(25*(x*%e^x*sin(x)+(1-x)*%e^x*cos(x))
+((-25*x-25)*%e^x-6*%e^(2*x))*sin(x)
+(8*%e^(2*x)+25*x*%e^x)*cos(x)+(50*x^2-200*x+300)*%e^x)
/50
+(%k2*x+%k1)*%e^-x
(%i4)

```