Only a, b, and c. Determine whether each of the following first-orde.pdf

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The document discusses three first-order differential equations and whether they are separable or not. Equation a) is separable and can be rewritten in separated form as dx/x^2 = (3 - sint)dt. Equation b) is also separable and can be rewritten in separated form as dx = (3t - ysin(t)) dt. Equation c) is determined to not be separable.

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Only a, b, and c. Determine whether each of the following first-order equations is or is not
separable. If the equation is separable, rewrite it in the form of equation.
Solution
a)
dx/dt = 3x^2 - x^2*sint
dx/dt = x^2(3 - sint)
dx = x^2 * (3 - sint) * dt
dx/x^2 = (3 - sint)*dt ----> separated form
b)
dx/dt = 3t - ysin(t)
dx = (3t - ysin(t)) * dt ---> separated form
c)
Not separable

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