Calc3pp15-20 MRG 2012.0524

3464 days ago by calcpage123

# when does x'+x-1=0? var('t') de = lambda x:diff(x,t)+x-1 show(de(sin(t))) show(de(e^t)) show(de(t^2)) show(de(e^(-t))) show(de(1)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(t\right) + \cos\left(t\right) - 1
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, e^{t} - 1
\newcommand{\Bold}[1]{\mathbf{#1}}t^{2} + 2 \, t - 1
\newcommand{\Bold}[1]{\mathbf{#1}}-1
\newcommand{\Bold}[1]{\mathbf{#1}}0
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(t\right) + \cos\left(t\right) - 1
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, e^{t} - 1
\newcommand{\Bold}[1]{\mathbf{#1}}t^{2} + 2 \, t - 1
\newcommand{\Bold}[1]{\mathbf{#1}}-1
\newcommand{\Bold}[1]{\mathbf{#1}}0
# solve x'+ x -1 = 0 var('t') x=function('x',t) desolve(diff(x,t)+x-1,x,[0,-5]) 
       
(e^t - 6)*e^(-t)
(e^t - 6)*e^(-t)
var('y') l=sqrt(1+(1-y)^2) p1=plot_vector_field((1/l,(1-y)/l),(x,-2,10),(y,-45,10)) f(x)=(e^x-6)*e^(-x) p2=plot(f(x),xmin=-2,xmax=10) p1+p2 
       
# solve x" + x = 0 var('t') x=function('x',t) show(desolve(diff(x,t,2)+x,x)) show(desolve(diff(x,t,2)+x,x,[0,0,1])) show(desolve(diff(x,t,2)+x,x,[pi/4,1,-1])) a=plot(desolve(diff(x,t,2)+x,x,[0,0,1]),xmin=0,xmax=pi,color='red') b=plot(desolve(diff(x,t,2)+x,x,[pi/4,1,-1]),xmin=0,xmax=pi,color='green') c=plot([-t+pi/4+1],xmin=0,xmax=pi) d=plot([t],xmin=0,xmax=pi) show(a+b+c+d,aspect_ratio=1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}k_{1} \sin\left(t\right) + k_{2} \cos\left(t\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(t\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{2} \cos\left(t\right)
\newcommand{\Bold}[1]{\mathbf{#1}}k_{1} \sin\left(t\right) + k_{2} \cos\left(t\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(t\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{2} \cos\left(t\right)
#p20) solve: x"+4x'+4x=0 show(desolve(diff(x,t,2)+4*diff(x,t,1)+4*x,x)) show(desolve(diff(x,t,2)+4*diff(x,t,1)+4*x,x,[0,0,1])) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(k_{2} t + k_{1}\right)} e^{\left(-2 \, t\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}t e^{\left(-2 \, t\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(k_{2} t + k_{1}\right)} e^{\left(-2 \, t\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}t e^{\left(-2 \, t\right)}