• Solve the following differential equation xdy - ydx = 0

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:

y(x) = c_1 x

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step-by-step explanation: