Answer:
y(x) = c_1 x
Step-by-step explanation:
Solve the separable equation x ( dy(x))/( dx) - y(x) = 0:
Solve for ( dy(x))/( dx):
( dy(x))/( dx) = y(x)/x
Divide both sides by y(x):
(( dy(x))/( dx))/y(x) = 1/x
Integrate both sides with respect to x:
integral(( dy(x))/( dx))/y(x) dx = integral1/x dx
Evaluate the integrals:
log(y(x)) = log(x) + c_1, where c_1 is an arbitrary constant.
Solve for y(x):
y(x) = e^(c_1) x
Simplify the arbitrary constants:
Answer: y(x) = c_1 x
