DE

102 days ago by jhlee2chn

Example 4

var('k,t') y = function('y',t) de = diff(y,t) == k*y desolve(de,[y,t]) 
       
c*e^(k*t)
c*e^(k*t)
var('H') solve(e^(k*H)==0.5, k) 
       
[k == -log(2)/H]
[k == -log(2)/H]
(-log(2)/5715).n(digits=5) 
       
-0.00012129
-0.00012129
solve(e^(-log(2)/5715*t) == 0.525, t) 
       
[t == 5715*log(40/21)/log(2)]
[t == 5715*log(40/21)/log(2)]
(5715*log(40/21)/log(2)).n(digits=5) 
       
5312.7
5312.7

Example 6

var('w,x') assume(w > 0) y = function('y',x) de = diff(y,x,2) + w^2*y == 0 desolve(de,[y,x]) 
       
k1*sin(w*x) + k2*cos(w*x)
k1*sin(w*x) + k2*cos(w*x)

Example 1  Laplace Transform

var('s, t') f(t) = 1 print f(t).laplace(t, s) 
       
1/s
1/s
g(t) = t print g(t).laplace(t, s) 
       
s^(-2)
s^(-2)