In [1]:

    

import sympy as sp
sp.init_printing()


    

In [13]:

    

x, y, k = sp.symbols('x y k')
f = sp.Function('f')


    

In [6]:

    

sp.Integral(f(x), x)


    

    
Out[6]:





$$\int f{\left (x \right )}\, dx$$

In [7]:

    

sp.Derivative(f(x), x)


    

    
Out[7]:





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

In [8]:

    

sp.diff(f(x),x)


    

    
Out[8]:





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

In [9]:

    

sp.diff(x**2, x)


    

    
Out[9]:





$$2 x$$

In [14]:

    

sp.dsolve(sp.diff(f(x)) - k*f(x), f(x))


    

    
Out[14]:





$$f{\left (x \right )} = C_{1} e^{k x}$$

In [25]:

    

sol = sp.dsolve(sp.Derivative(f(x),x) - k*f(x), f(x));
sol


    

    
Out[25]:





$$f{\left (x \right )} = C_{1} e^{k x}$$

In [33]:

    

const_sol = sol.subs(x,0).subs(f(0),1);
const_sol


    

    
Out[33]:





$$1 = C_{1}$$

In [40]:

    

sol.subs(const_sol.args[1], const_sol.args[0])


    

    
Out[40]:





$$f{\left (x \right )} = e^{k x}$$

In [ ]: