from sympy import *
f = symbols('f', cls=Function)
x = symbols('x')
eq = Eq(f(x).diff(x, x) - 2*f(x).diff(x) + f(x), sin(x))
print(dsolve(eq, f(x)))

from sympy import *
f = symbols('f', cls=Function)
x = symbols('x')
eq = Eq(f(x).diff(x,1)+f(x)+f(x)**2, 0)
print(dsolve(eq, f(x)))
C1 = symbols('C1')
eqr = -C1/(C1 - exp(x))
eqr1 = eqr.subs(x, 0)
print(solveset(eqr1 - 1, C1))
eqr2 = eqr.subs(C1, 1/2)
# 画图
import matplotlib.pyplot as plt
import numpy as np
x_1 = np.arange(-5, 5, 0.1)
y_1 = [-0.5/(0.5 - exp(x)) for x in x_1]
plt.plot(x_1, y_1)
plt.axis([-6,6,-10,10])
plt.grid()
plt.show()

from sympy import *
y = symbols('y', cls=Function)
x = symbols('x')
eq = Eq(y(x).diff(x,1), y(x))
print(dsolve(eq, y(x)))
C1 = symbols('C1')
eqr = C1*exp(x)
eqr1 = eqr.subs(x, 0)
print(solveset(eqr1 - 1, C1))
eqr2 = eqr.subs(C1, 1)
# 画图
import matplotlib.pyplot as plt
import numpy as np
x_1 = np.arange(-5, 5, 0.01)
y_1 = [exp(x) for x in x_1]
plt.plot(x_1, y_1, color='orange')
plt.grid()
plt.show()