Mathematics, 01.07.2020 15:01 182075
A homogeneous second-order linear differential equation, two functions y 1y1 and y 2y2, and a pair of initial conditions are given. First verify that y 1y1 and y 2y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x.
y'' + 49y = 0; y1 = cos(7x) y2 = sin(7x); y(0) = 10 y(0)=-4
1.Why is the function y, = e * a solution to the differential equation?
A. The function y1 =e 4X is a solution because when the function and its indefinite integral, , are substituted into the equation, the result is a true statement.
B. The function y1 = e 4X is a solution because when the function and its second derivative, y1" = 16 e 4x, are substituted into the equation, the result is a true statement.
2. Why is the function y2 solution the differential equation?
A. The function y2 = e 4x is a solution because when the function and its indefinite integral, are substituted into the equation, the result a true statement. The function y2 = e 4X is a solution because when the function and its second derivative, y2" = 16 e -4x are substituted into the equation, the result is a true statement. The particular solution of the form y = c, y, +c, y2 that satisfies the initial conditions y(0) 2 and y'(0) = 9 is y =.
Answers: 3
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A homogeneous second-order linear differential equation, two functions y 1y1 and y 2y2, and a pair o...
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