Concept explainers
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. The general solution of a second-order linear differential equation could be y = ce2t – t2, where c is an arbitrary constant.
b. If yh is a solution of a homogeneous differential equation y" + py' + qy = 0 and yp is a particular solution of the equation y″ + py′ + qy = f, then yp + cyh is also a particular solution, for any constant c.
c. The functions {l – cos2 x, 5 sin2 x} are linearly independent on the interval [0, 2π].
d. If y1 and y2 are solutions of the equation y" + yy' = 0, then y1 + y2 is also a solution of the equation.
e. The initial value problem y" + 2y = 0, y(0) = 4 has a unique solution.
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Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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