#Uebung 3.6#1a)fa:=(x) -> exp(-x)+2^(-x)+2*cos(x)-6: plot(fa(x), x=-1.5..1); fsolve(fa=0);

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

NiMkISs3N1t6NSEiKg==

#1b)fb:=(x) -> exp(6*x)+3*(ln(2))^2*exp(2*x)-ln(8)*exp(4*x)-(ln(2))^3: plot(fb(x), x=-.5..0); fsolve(fb=0);

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

NiMkISslZmtEJD0hIzU=

#2)with(DEtools): infolevel[dsolve]:=3; DG:=diff(y(x),x)+y(x)/x=x^2; bed:=y(1)=0: dsolve({DG,bed},y(x));

NiM+JkkqaW5mb2xldmVsR0koX3N5c2xpYkc2IjYjSSdkc29sdmVHNiRJKnByb3RlY3RlZEdGK0YmIiIkNiM+SSNER0c2Ii8sJi1JJWRpZmZHSSpwcm90ZWN0ZWRHRio2JC1JInlHRiU2I0kieEdGJUYvIiIiKiZGLEYwRi8hIiJGMCokRi8iIiM=

Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear <- 1st order linear successful NiMvLUkieUc2IjYjSSJ4R0YmKiYsJiokRigiIiUjIiIiRiwjISIiRixGLkYuRihGMA==

#3)ve:=sqrt( (7*9.81*2)/ (.6*.5*1.3) ) *3.6;

NiM+SSN2ZUc2IiQiK1NYbmJuISIp

#4)#a)DG:=diff(y(x),x)-2*y(x)=sin(x); dsolve(DG,y(x));

NiM+SSNER0c2Ii8sJi1JJWRpZmZHSSpwcm90ZWN0ZWRHRio2JC1JInlHRiU2I0kieEdGJUYvIiIiRiwhIiMtSSRzaW5HNiRGKkkoX3N5c2xpYkdGJUYuMethods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear <- 1st order linear successful NiMvLUkieUc2IjYjSSJ4R0YmLCgtSSRjb3NHNiRJKnByb3RlY3RlZEdGLUkoX3N5c2xpYkdGJkYnIyEiIiIiJi1JJHNpbkdGLEYnIyEiI0YxKiYtSSRleHBHRiw2IywkRigiIiMiIiJJJF9DMUdGJkY8Rjw=

#b)DG:=diff(x(t),t)+3*x(t)=t-1; dsolve(DG,x(t));

NiM+SSNER0c2Ii8sJi1JJWRpZmZHSSpwcm90ZWN0ZWRHRio2JC1JInhHRiU2I0kidEdGJUYvIiIiRiwiIiQsJkYvRjAhIiJGMA==

Methods for first order ODEs: --- Trying classification methods --- trying a quadrature trying 1st order linear <- 1st order linear successful

NiMvLUkieEc2IjYjSSJ0R0YmLChGKCMiIiIiIiQjISIlIiIqRisqJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0Y0SShfc3lzbGliR0YmNiMsJEYoISIkRitJJF9DMUdGJkYrRis=