I'm writing an @interact to solve simple 2nd order differential
equations and plot solutions. In it, I'd like to typeset the formula:
show(a*diff(y,t,2)+b*diff(y,t)+c==0)
However, what shows up is the word "diff" when I'd really like to see
math notation for a partial or total derivative (depending on the
independent variables declared for y). Is there a nice way to get it to
show up?
Note that just printing a string doesn't work so well, since a, b, or c
might be negative and then you get something like
3(d^2y/dt^2)+-2(dy/dt)+-3=0.
For reference, the current (non/barely) working code is:
var("x,t")
@interact
def _(y0=(0,4,1/5), y0p=(0,4,1/5),a=(-4,4,1/5),b=(-4,4,1/5),c=(-4,4,1/5)):
y=function('y',t)
show(a*diff(y,t,2)+b*diff(y,t)+c==0)
show(" y(0)=%s, y'(0)=%s"%(y0,y0p))
t0=0
discriminant = sqrt(b^2-4*a*c)
if discriminant > 0:
r1 = (-b+discriminant)/(2*a)
r2 = (-b-discriminant)/(2*a)
c1=(y0p-y0*r1)/(r1-r2)*e^(-r1*t0)
c2=(y0*r1-y0p)/(r1-r2)*e^(-r2*t0)
soln = c1*e^(r1*t)+c2*e^(r2*t)
show(soln)
plot(soln,(t,0,5)).show()
Thanks,
Jason
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