PKâXqXńB–Hmimetypetext/x-wxmathmlPKâXqXQdBV55 format.txt This file contains a wxMaxima session in the .wxmx format. .wxmx files are .xml-based files contained in a .zip container like .odt or .docx files. After changing their name to end in .zip the .xml and eventual bitmap files inside them can be extracted using any .zip file viewer. The reason why part of a .wxmx file still might still seem to make sense in a ordinary text viewer is that the text portion of .wxmx by default isn't compressed: The text is typically small and compressing it would mean that changing a single character would (with a high probability) change big parts of the whole contents of the compressed .zip archive. Even if version control tools like git and svn that remember all changes that were ever made to a file can handle binary files compression would make the changed part of the file bigger and therefore seriously reduce the efficiency of version control wxMaxima can be downloaded from https://github.com/wxMaxima-developers/wxmaxima. It also is part of the windows installer for maxima (https://wxmaxima-developers.github.io/wxmaxima/). If a .wxmx file is broken but the content.xml portion of the file can still be viewed using an text editor just save the xml's text as "content.xml" and try to open it using a recent version of wxMaxima. If it is valid XML (the XML header is intact, all opened tags are closed again, the text is saved with the text encoding "UTF8 without BOM" and the few special characters XML requires this for are properly escaped) chances are high that wxMaxima will be able to recover all code and text from the XML file. PKâXqX¶ĆS—źź content.xml Kedvenc Matematikai KĂ­sĂ©rleteim Alapok Halmazok Ă©s fĂŒggvĂ©nyek SzĂĄmok HatĂĄrĂ©rtĂ©k DifferenciĂĄlszĂĄmĂ­tĂĄs IntegrĂĄlszĂĄmĂ­tĂĄs LineĂĄris algebra TöbbvĂĄltozĂłs fĂŒggvĂ©nyek MĂ©rtĂ©k Ă©s valĂłszĂ­nƱsĂ©g Fourier-elmĂ©let Komplex fĂŒggvĂ©nytan KözönsĂ©ges differenciĂĄlegyenletek Alapfogalmak EgyvĂĄltozĂłs variĂĄciĂłszĂĄmĂ­tĂĄs Elemi megoldĂĄsi mĂłdszerek ÁltalĂĄnos eredmĂ©nyek LineĂĄris differenciĂĄlegyenletek LineĂĄris alapproblĂ©ma TĂ©tel SzuperpozĂ­ciĂł, komplexifikĂĄlĂĄs Alaprendszer TĂ©tel A konstans variĂĄlĂĄsa TĂ©tel A csatolĂĄs csökkentĂ©se DefinĂ­ciĂł TĂ©tel TĂ©tel KonstansegyĂŒtthatĂłs egyenlet Feladat (1) kill(all); (%o0) done load("eigen"); (%o1) /usr/share/maxima/5.43.2/share/matrix/eigen.mac a:matrix([1,2],[2,4]); (%o2) 1224 eivals(a); (%o3) [[0,5],[1,1]] x1:c11*exp(0*t)+c12*exp(5*t); x2:c21*exp(0*t)+c22*exp(5*t); (%o4) c12*%e5*t+c11(%o5) c22*%e5*t+c21 solve([diff(x1,t)=x1+2*x2,diff(x2,t)=2*x1+4*x2, subst(t=0,x1)=5,subst(t=0,x2)=5],[c11,c12,c21,c22]); (%o6) [[c11=2,c12=3,c21=−1,c22=6]] subst(%[1],[x1,x2]); (%o7) [3*%e5*t+2,6*%e5*t−1] vagy kill(all); (%o0) done load("ode2"); (%o1) /usr/share/maxima/5.43.2/share/diffequations/ode2.mac eq1:'diff(x1(t),t)=x1(t)+2*x2(t); (%o2) dd*t*x1

t

=2*x2

t

+x1

t

eq2:'diff(x2(t),t)=2*x1(t)+4*x2(t); (%o3) dd*t*x2

t

=4*x2

t

+2*x1

t

atvalue(x1(t),t=0,5); (%o4) 5 atvalue(x2(t),t=0,5); (%o5) 5 desolve([eq1,eq2],[x1(t),x2(t)]); (%o6) [x1

t

=3*%e5*t+2,x2

t

=6*%e5*t−1]
(2) a:matrix([5,2],[-8,-3]); (%o9) 52−8−3 eivals(a); (%o10) [[1],[2]] x1:c11*exp(t)+c12*t*exp(t); x2:c21*exp(t)+c22*t*exp(t); (%o11) c12*t*%et+c11*%et(%o12) c22*t*%et+c21*%et solve([diff(x1,t)=5*x1+2*x2,diff(x2,t)=-8*x1-3*x2, subst(t=0,x1)=-3,subst(t=0,x2)=2],[c11,c12,c21,c22]); (%o13) [[c11=−3,c12=−8,c21=2,c22=16]] subst(%[1],[x1,x2]); (%o14) [−8*t*%et−3*%et,16*t*%et+2*%et] etc. MagasabbrendƱ lineĂĄris differenciĂĄlegyenlet TĂ©tel MegjegyzĂ©s Az adjungĂĄlt egyenlet AdjungĂĄlt egyenlet magasabbrendƱ lineĂĄris egyenletekre Vegyes mĂłdszerek Feladat kill(all); (%o0) done load("ode2"); (%o1) /usr/share/maxima/5.43.2/share/diffequations/ode2.mac (1) eq:x*'diff(y,x,2)+2*x*'diff(y,x)-x*y; (%o15) x*

d2d*x2*y

+2*x*

dd*x*y

−x*y
eq:ratsimp(eq/x); (%o16) d2d*x2*y+2*

dd*x*y

−y
(2) φ:x MĂĄs jelölĂ©ssel φ:t; (%o9) t xp:t*y+∫y; (%o10) ∫y+t*y xpp:t*yp+y+y; (%o11) t*yp+2*y (2*t+1)*xpp+4*t*xp-4*t*∫y; (%o12) 4*t*

∫y+t*y

−4*t*∫y+

2*t+1

*

t*yp+2*y

expand(%); (%o13) 2*t2*yp+t*yp+4*t2*y+4*t*y+2*y eq:subst(yp='diff(y,t),%); (%o14) 2*t2*

dd*t*y

+t*

dd*t*y

+4*t2*y+4*t*y+2*y
ode2(eq,y,t); (%o15) y=%c*

2*t+1

*%e−2*t
t2
(3) φ:exp(x); (%o10) %ex etc. (4) y:a_0+a_1*x+a_2*x^2; (%o7) a2*x2+a1*x+a0 x*(x-1)*diff(y,x,2)-x*diff(y,x)+y; (%o8) a2*x2−x*

2*a2*x+a1

+2*a2*

x−1

*x+a1*x+a0
expand(%); (%o9) a2*x2−2*a2*x+a0 φ:x; (%o10) x etc. (5) y:tan(x); (%o22) tan

x

diff(y,x,2)-2*(1+(tan(x)^2))*y; (%o25) 2*sec

x

2
*tan

x

−2*tan

x

*

tan

x

2+1

trigsimp(%); (%o26) 0 φ:tan(x); (%o27) tan

x

etc. (6) Integrålunk: 0=(exp(x)+1)*y'-∫exp(x)*y'-2*y-∫exp(x)*y =(exp(x)+1)*y'-exp(x)*y+∫exp(x)*y-2*y =(exp(x)+1)*y'-(exp(x)+2)*y etc. Feladat (1) Az inhomogén egy megoldåsa y=x. A homogént integråljuk: 0=(x^2-1)*y'-∫2*x*y'+4*x*y-∫4*y+∫2*y =(x^2-1)*y'-2*x*y+∫2*y+4x*y-∫4*y+∫2*y =(x^2-1)*y'-2*x*y ode2((x^2-1)*'diff(y,x)-2*x*y,y,x); (%o2) y=%c*

x2−1

etc. (2) kill(all); (%o0) done A vĂĄltozĂłt t-re, az ismeretlent x-re cserĂ©lve, az adjungĂĄlt egyenlet: a0:-6*t; a1:2; a2:3*t^3+t; b:4-12*t^2; (%o1) −6*t(%o2) 2(%o3) 3*t3+t(%o4) 4−12*t2 depends(y,t); (%o5) [y

t

]
aeq:a0*y-diff(a1*y,t)+diff(a2*y,t,2); (%o6)

3*t3+t

*

d2d*t2*y

+2*

9*t2+1

*

dd*t*y

−2*

dd*t*y

+12*t*y
ratsimp(%); (%o7)

3*t3+t

*

d2d*t2*y

+18*t2*

dd*t*y

+12*t*y
aeq:%/t; (%o8)

3*t3+t

*

d2d*t2*y

+18*t2*

dd*t*y

+12*t*y
t
ratsimp(%); (%o9)

3*t2+1

*

d2d*t2*y

+18*t*

dd*t*y

+12*y
aeq:%; (%o10)

3*t2+1

*

d2d*t2*y

+18*t*

dd*t*y

+12*y
Integråljuk: 0=(3*t^2+1)*y'-∫6*t*y'+18*t*y-∫18*y+∫12*t =(3t*2+1)*y'-6*t*y+∫6*y+18*t*y-∫18*y+∫12*y =(3t^2+1)*y'+12*t*y load("ode2"); (%o11) /usr/share/maxima/5.43.2/share/diffequations/ode2.mac ode2((3*t^2+1)*'diff(y,t)+12*t*y,y,t); (%o12) y=%c

3*t2+1

2
y:subst(%c=1,rhs(%)); (%o13) 1

3*t2+1

2
eq:y*a0*'diff(x,t)-diff(a0*y,t)*x+y*a1*x=c+integrate(b*y,t); (%o48) −6*t*

dd*t*x

3*t2+1

2
+2*x

3*t2+1

2
−

72*t2

3*t2+1

3−6

3*t2+1

2

*x=4*t3*t2+1+c
eq:eq*(3*t^2+1)^3; (%o49)

3*t2+1

3
*

−6*t*

dd*t*x

3*t2+1

2
+2*x

3*t2+1

2
−

72*t2

3*t2+1

3−6

3*t2+1

2

*x

=

3*t2+1

3
*

4*t3*t2+1+c

ratsimp(%); (%o50)

−18*t3−6*t

*

dd*t*x

+

8−48*t2

*x=27*c*t6+36*t5+27*c*t4+24*t3+9*c*t2+4*t+c
eq:%; (%o51)

−18*t3−6*t

*

dd*t*x

+

8−48*t2

*x=27*c*t6+36*t5+27*c*t4+24*t3+9*c*t2+4*t+c
ode2(eq,x,t); (%o52) x=%e4*log

t

3
*

%c−3*

166320t+201960*ct2+257040t3+176715*ct4+188496t5+157080*ct6+106029*c

*%e20*log

t

3
26180
−3*

16*%e−log

t

3
+c*%e−4*log

t

3

46

3*t2+1

2
(3) y:a_0+a_1*x+a_2*x^2; (x+1)*x*diff(y,x,2)+(x+2)*diff(y,x)-y; (%o29) −a2*x2+

x+2

*

2*a2*x+a1

+2*a2*x*

x+1

−a1*x−a0
expand(%); (%o30) 3*a2*x2+6*a2*x+2*a1−a0 y:x+2; (%o35) x+2 (x+1)*x*diff(y,x,2)+(x+2)*diff(y,x)-y; (%o36) 0 φ:x+2; (%o41) x+2 etc. Feladat kill(all); (%o0) done (1) solve(λ^2-λ-2,λ); (%o1) [λ=2,λ=−1] c1*exp(2*x)+c2*exp(-x); (%o2) c1*%e2*x+c2*%e−x vagy load("ode2"); (%o2) /usr/share/maxima/5.43.2/share/diffequations/ode2.mac e:'diff(y(x),x,2)+'diff(y(x),x)-2*y(x)=0; (%o7) d2d*x2*y

x

+dd*x*y

x

−2*y

x

=0
desolve(e,y(x)); (%o8) y

x

=%ex*

dd*x*y

x

x=0+2*y

0

3
−%e−2*x*

dd*x*y

x

x=0−y

0

3
etc. Feladat ode2('diff(y,x,2)+y=0,y,x); (%o14) y=%k1*sin

x

+%k2*cos

x

bc2(%,x=0,y=0,x=%pi/2,y=1); (%o15) y=sin

x

Feladat (1) eq:'diff(y(x),x,2)-y(x)/x^2=0; (%o21) d2d*x2*y

x

−y

x

x2
=0
eq:eq*x^2; (%o22) x2*

d2d*x2*y

x

−y

x

x2

=0
eq:ratsimp(eq); (%o23) x2*

d2d*x2*y

x

−y

x

=0
desolve(eq,y(x)); (%o24) y

x

=ilt

−g210672*

d2d*g210672*laplace

y

x

,x,g21067

,g21067,x

+ilt

−4*g21067*

dd*g21067*laplace

y

x

,x,g21067

,g21067,x

helyett inkåbb x=exp(s) helyettesítéssel eq:'diff(w(s),s,2)-w(s); (%o1) d2d*s2*w

s

−w

s

desolve(eq,w(s)); (%o3) w

s

=%es*

dd*s*w

s

s=0+w

0

2
−%e−s*

dd*s*w

s

s=0−w

0

2
etc.
PKâXqXńB–HmimetypePKâXqXQdBV55 5format.txtPKâXqX¶ĆS—źź ’content.xmlPK§ÀŽ