DGLrestart;with(DEtools):# Neben dsolve sind n\374tzliche Funktionen:## dfieldplot(): Richtungsfeld# DEplot() : Richtungsfeld und spezielle L\366sunginfolevel[dsolve]:=3;

NiM+JkkqaW5mb2xldmVsR0koX3N5c2xpYkc2IjYjSSdkc29sdmVHNiRJKnByb3RlY3RlZEdGK0YmIiIk

#8.5 dgl1:=diff(y(x),x)-3*x-2*y(x)=1;

NiM+JSVkZ2wxRy8sKC0lJWRpZmZHNiQtJSJ5RzYjJSJ4R0YtIiIiKiYiIiRGLkYtRi4hIiIqJiIiI0YuRipGLkYxRi4=

dsolve(dgl1);

Methods for first order ODEs:--- Trying classification methods ---trying a quadraturetrying 1st order linear<- 1st order linear successfulNiMvLSUieUc2IyUieEcsKCooIiIkIiIiIiIjISIiRidGK0YtIyIiJiIiJUYtKiYtJSRleHBHNiMsJComRixGK0YnRitGK0YrJSRfQzFHRitGKw==

eigenschaften:=odeadvisor(dgl1); separierbar:=odeadvisor(dgl1,[separable]);

NiM+JS5laWdlbnNjaGFmdGVuRzcjNyQlKF9saW5lYXJHJShjbGFzc35BRw==NiM+JSxzZXBhcmllcmJhckc3IyUlTk9ORUc=

de := x*diff(y(x),x)+y(x)=ln(x)+1; odeadvisor(de);

NiM+JSNkZUcvLCYqJiUieEciIiItJSVkaWZmRzYkLSUieUc2I0YoRihGKUYpRi1GKSwmLSUjbG5HRi9GKUYpRik=NiM3IyUoX2xpbmVhckc=

de:=diff(y(x),x)+x/y(x)=sin(3*x)+diff(y(x),x); odeadvisor(de,[separable]);

NiM+JSNkZUcvLCYtJSVkaWZmRzYkLSUieUc2IyUieEdGLSIiIiomRi1GLkYqISIiRi4sJi0lJHNpbkc2IywkKiYiIiRGLkYtRi5GLkYuRidGLg==Error, (in ODEtools/info) Required a specification of the indeterminate function

de:=diff(y(x),x)+5*y(x)=2*x-1; odeadvisor(de,[separable]); dsolve(de);

NiM+JSNkZUcvLCYtJSVkaWZmRzYkLSUieUc2IyUieEdGLSIiIiomIiImRi5GKkYuRi4sJiomIiIjRi5GLUYuRi5GLiEiIg==NiM3IyUlTk9ORUc=Methods for first order ODEs:--- Trying classification methods ---trying a quadraturetrying 1st order linear<- 1st order linear successfulNiMvLSUieUc2IyUieEcsKCooIiIjIiIiIiImISIiRidGK0YrIyIiKCIjREYtKiYtJSRleHBHNiMsJComRixGK0YnRitGLUYrJSRfQzFHRitGKw==

de:=diff(y(x),x)-2*y(x)=cos(x)+x^2+1; odeadvisor(de,[separable]); dsolve(de);

NiM+JSNkZUcvLCYtJSVkaWZmRzYkLSUieUc2IyUieEdGLSIiIiomIiIjRi5GKkYuISIiLCgtJSRjb3NHRixGLiokKUYtRjBGLkYuRi5GLg==NiM3IyUlTk9ORUc=Methods for first order ODEs:--- Trying classification methods ---trying a quadraturetrying 1st order linear<- 1st order linear successfulNiMvLSUieUc2IyUieEcsLiomIyIiIyIiJiIiIi0lJGNvc0dGJkYtISIiKiYjRi1GLEYtLSUkc2luR0YmRi1GLSomRitGMEYnRitGMComRitGMEYnRi1GMCMiIiQiIiVGMComLSUkZXhwRzYjLCQqJkYrRi1GJ0YtRi1GLSUkX0MxR0YtRi0=

#Uebung 3.2.4a) de:=diff(y(x),x)+y(x)/x=(y(x))^3; odeadvisor(de,[separable]); intfactor(de); dsolve(de,y(x)); dsolve( de, y(x), [homogeneous], implicit );

NiM+SSNkZUc2Ii8sJi1JJWRpZmZHSSpwcm90ZWN0ZWRHRio2JC1JInlHRiU2I0kieEdGJUYvIiIiKiZGLEYwRi8hIiJGMCokRiwiIiQ=NiM3I0klTk9ORUc2Ig==, -> Computing symmetries using: way = 2 NiM3JCIiISomLCYqJkkieUc2IiIiIkkieEdGKUYqRioqJkYoIiIkRisiIiMhIiNGKkYrISIi, <- successful computation of symmetries. NiMqJi1JInlHNiI2I0kieEdGJiEiIiwmRikiIiIqJkYkIiIjRihGK0YtRik=Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear trying Bernoulli <- Bernoulli successful NiQvLUkieUc2IjYjSSJ4R0YmKiQsJkYoIiIjKiZGKEYrSSRfQzFHRiYiIiJGLiMhIiJGKy9GJCwkRilGMA==

Classification methods on request Methods to be used are: [homogeneous] ---------------------------- * Tackling ODE using method: homogeneous --- Trying classification methods --- trying homogeneous types:

trying homogeneous G

<- homogeneous successful NiMvLCotSSNsbkc2JEkqcHJvdGVjdGVkR0YoSShfc3lzbGliRzYiNiNJInhHRioiIiJJJF9DMUdGKiEiIi1GJjYjLCZGL0YtKiYtSSJ5R0YqRisiIiNGLEYtRjZGLy1GJjYjKiZGNEYtRiwjRi1GNkY2IiIh

evalf(exp(1));

NiMkIitHPUc9RiEiKg==

#Pruefung 1) de:=diff(y(x),x)*(1+x^2)*sin(y(x))-2*x*cos(y(x))=0; odeadvisor(de,[separable]); intfactor(de); dsolve(de,y(x)); dsolve( de, y(x), [homogeneous], implicit );

NiM+SSNkZUc2Ii8sJiooLUklZGlmZkdJKnByb3RlY3RlZEdGKzYkLUkieUdGJTYjSSJ4R0YlRjAiIiIsJkYxRjEqJEYwIiIjRjFGMS1JJHNpbkc2JEYrSShfc3lzbGliR0YlNiNGLUYxRjEqJkYwRjEtSSRjb3NHRjdGOUYxISIjIiIh

NiM3I0krX3NlcGFyYWJsZUc2Ig==

NiMiIiI=Methods for first order ODEs: --- Trying classification methods ---

trying a quadrature trying 1st order linear trying Bernoulli trying separable <- separable successful

NiMvLUkieUc2IjYjSSJ4R0YmLUknYXJjY29zRzYkSSpwcm90ZWN0ZWRHRixJKF9zeXNsaWJHRiY2IyomSSRfQzFHRiYiIiIsJkYxRjEqJEYoIiIjRjEhIiI=Classification methods on request Methods to be used are: [homogeneous] ---------------------------- * Tackling ODE using method: homogeneous --- Trying classification methods --- trying homogeneous types:

de:=diff(y(x),x)-x*diff(y(x),x)-y(x)+(x-1)^2=0;

NiM+SSNkZUc2Ii8sKi1JJWRpZmZHSSpwcm90ZWN0ZWRHRio2JC1JInlHRiU2I0kieEdGJUYvIiIiKiZGL0YwRihGMCEiIkYsRjIqJCwmRi9GMEYyRjAiIiNGMCIiIQ==

eigenschaften:=odeadvisor(de); separierbar:=odeadvisor(de,[separable]); intfactor(de); dsolve(de,y(x));

NiM+SS5laWdlbnNjaGFmdGVuRzYiNyNJKF9saW5lYXJHRiU=NiM+SSxzZXBhcmllcmJhckc2IjcjSSVOT05FR0Yl

NiMiIiI=Methods for first order ODEs:

--- Trying classification methods --- trying a quadrature trying 1st order linear

<- 1st order linear successful NiMvLUkieUc2IjYjSSJ4R0YmKiYsJiokLCZGKCIiIiEiIkYtIiIkI0YtRi9JJF9DMUdGJkYtRi1GLEYu

de:=diff(y(x),x)-y(x)=x/(3*y(x)^2);

NiM+SSNkZUc2Ii8sJi1JJWRpZmZHSSpwcm90ZWN0ZWRHRio2JC1JInlHRiU2I0kieEdGJUYvIiIiRiwhIiIsJComRi9GMEYsISIjI0YwIiIk

eigenschaften:=odeadvisor(de); separierbar:=odeadvisor(de,[separable]); intfactor(de); dsolve(de,y(x));

NiM+SS5laWdlbnNjaGFmdGVuRzYiNyRJKl9yYXRpb25hbEdGJUkrX0Jlcm5vdWxsaUdGJQ==NiM+SSxzZXBhcmllcmJhckc2IjcjSSVOT05FR0Yl, -> Computing symmetries using: way = 2

NiM3JCIiISwkKiYsKCIiIkYoSSJ4RzYiIiIkKiRJInlHRipGKyIiKkYoRi0hIiMjRihGKw==, <- successful computation of symmetries. NiMqJi1JInlHNiI2I0kieEdGJiIiIywoIiIiRitGKCIiJCokRiRGLCIiKiEiIg==Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear trying Bernoulli <- Bernoulli successful

NiUvLUkieUc2IjYjSSJ4R0YmLCQqJCwoISIkIiIiRighIioqJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YzSShfc3lzbGliR0YmNiMsJEYoIiIkRi1JJF9DMUdGJkYtIiNGI0YtRjdGOi9GJCwmRiojISIiIiInKiheI0Y9Ri1GNyNGLSIiI0YrRjpGLS9GJCwmRipGPSooXiMjRi1GP0YtRjdGQkYrRjpGLQ==