DE -- Sage

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)

DE