from sympy import *
from IPython.display import display
x,y,z, t,n = symbols('x y z t n')

Equações

eqc = Eq(x * (x-2)**2 * (x-5),0)


display(eqc)
print('Soluções:',solve(eqc))
print('Raízes :',roots(eqc))

$\displaystyle x \left(x - 5\right) \left(x - 2\right)^{2} = 0$

Soluções: [0, 2, 5]
Raízes : {5: 1, 2: 2, 0: 1}

eqc = Eq(x**2 + y**2,oo)
display(eqc)

$\displaystyle x^{2} + y^{2} = \infty$

eqc = Eq(x**2 + y**2,10)
display(eqc)

display(solveset(eqc,x,domain=Reals))

$\displaystyle x^{2} + y^{2} = 10$

$\displaystyle \mathbb{R} \cap \left\{- \sqrt{10 - y^{2}}, \sqrt{10 - y^{2}}\right\}$

eqs1 = [Eq(x*2 + 5*y,x + 10),Eq(x-y,y)]
for i in eqs1: display(i)
print('Soluções:',solve(eqs1))

print('\n\n')
eqs2 = [Eq(x*y - 1,x),Eq(x-2,y), Eq(z*10+2*y,E)]
for i in eqs2: display(i)
a = solve(eqs2)
print('Soluções:',solve(eqs2))

$\displaystyle 2 x + 5 y = x + 10$

$\displaystyle x - y = y$

Soluções: {x: 20/7, y: 10/7}

$\displaystyle x y - 1 = x$

$\displaystyle x - 2 = y$

$\displaystyle 2 y + 10 z = e$

Soluções: [{x: 3/2 - sqrt(13)/2, y: -sqrt(13)/2 - 1/2, z: 1/10 + E/10 + sqrt(13)/10}, {x: 3/2 + sqrt(13)/2, y: -1/2 + sqrt(13)/2, z: -sqrt(13)/10 + 1/10 + E/10}]

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Equações Diferenciais

f,g,h = symbols('f g h', cls=Function)

display(Derivative(f(x),x))
display(f(x).diff(x))

$\displaystyle \frac{d}{d x} f{\left(x \right)}$

$\displaystyle \frac{d}{d x} f{\left(x \right)}$

eq1 = Eq(f(x).diff(x,2) - f(x).diff(x) + f(x),E**x + 30*x)
display(eq1)
print()
display(dsolve(eq1))

$\displaystyle f{\left(x \right)} - \frac{d}{d x} f{\left(x \right)} + \frac{d^{2}}{d x^{2}} f{\left(x \right)} = 30 x + e^{x}$

$\displaystyle f{\left(x \right)} = 30 x + \left(C_{1} \sin{\left(\frac{\sqrt{3} x}{2} \right)} + C_{2} \cos{\left(\frac{\sqrt{3} x}{2} \right)}\right) e^{\frac{x}{2}} + e^{x} + 30$

eq2 = Eq(f(x).diff(x,2), f(x) * g(y))
display(eq2)

print()

soluc = dsolve(eq2)
display('Solução:',soluc)

print('\n\n')

display('x = 2',
        soluc.subs('x',2))

print('\n\n')

display('x = 5, C1 = log(5), C2 = 0',
        soluc.subs([('x',5),('C1',log(5)),('C2',0)])
    )

$\displaystyle \frac{d^{2}}{d x^{2}} f{\left(x \right)} = f{\left(x \right)} g{\left(y \right)}$

'Solução:'

$\displaystyle f{\left(x \right)} = C_{1} e^{- x \sqrt{g{\left(y \right)}}} + C_{2} e^{x \sqrt{g{\left(y \right)}}}$

'x = 2'

$\displaystyle f{\left(2 \right)} = C_{1} e^{- 2 \sqrt{g{\left(y \right)}}} + C_{2} e^{2 \sqrt{g{\left(y \right)}}}$

'x = 5, C1 = log(5), C2 = 0'

$\displaystyle f{\left(5 \right)} = e^{- 5 \sqrt{g{\left(y \right)}}} \log{\left(5 \right)}$