Substitution for differential equations

[Alexishul]

Hello,

For a project dealing with differential equations, i would like to replace all the variables "y" of my differential equation with another expression, like the sympy.subs() method actually does.

However i want to get totally rid of Sympy and only use Mathics.
Is this possible ? I started to look into "Rule" and "Pattern" classes, but i didn't really understand...

Here's an example of what i expect :

session = MathicsSession()

x = Symbol("x")
y = Symbol("y")

eq1str = "Derivative[y, {x, 2}] + 100 * y"
eq1 = session.evaluate(eq1str).to_python()

eq2str = "cos(x) + x**2"
eq2 = session.evaluate(eq2str).to_python()

#Here : in "eq1" replace "y" by "eq2

[mmatera]

Usually, in WMA, I make the replace like this:

eq1/.{y->(Cos[#1]+#1^2)&}

The reason to use an anonymous function is that in the equation, D[y[x],{x,2]] is evaluated as Derivative[2][y][x], so

eq1= y''[x]+y[x]==0

actually stores in eq1

eq1= Derivative[2][y][x]+y[x]==0

Then, to get the equation evaluated, y must be replaced by something that can be applied over the argument x:

(Cos[#1]+#1^2)&[x] === Cos[x]+x^2

[Alexishul]

So, if I understand well, on Python, this should be correct ?

eq1str = "Derivative[y, {x, 2}] + 100 * y"
eq1 = session.evaluate(eq1str).to_python()

eq2str = "5 * x"
eq2 = session.evaluate(eq2str).to_python()

#Here : in "eq1" replace "y" by "eq2

eq3str = eq1str + "/.{y->(" + eq2str + ")}"
eq3 = session.evaluate(eq3str).to_python()
print(eq3)

Here is the output :

System`Plus[System`Times[500, Global`x], System`Derivative[System`Times[5, Global`x], {Global`x,2}]]`

which means :

500x + (5x)''

Tell me if i'm wrong, and if not, how can i simplify this result ?
(the simplification (5x)'' = 0)