Consider the first-order equation and the second-order equation
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Consider the first-order equation dxdy=x and the second-order equation dx2d2y=x. Which statement about their general solutions is most accurate?
(a) Both general solutions contain one arbitrary constant, because you add “+C” only once after integrating.
(b) Neither general solution contains any arbitrary constants, since x rather than y appears on the right side.
(c) The first‐order equation's general solution contains one arbitrary constant, whereas the second‐order equation's contains two.
(d) The first‐order equation's general solution contains two arbitrary constants, whereas the second‐order equation's contains one.