Solution Found!
The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous
Chapter 3, Problem 23(choose chapter or problem)
The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y__ + p(t) y_ + q(t) y = g(t), (38) provided one solution y1 of the corresponding homogeneous equation is known. Let y = v(t) y1(t) and show that y satisfies equation (38) if v is a solution of y1(t)v__ + 2y_ 1(t) + p(t) y1(t)v_ = g(t). (39) Equation (39) is a first-order linear differential equation for v_. By solving equation (39) for v_, integrating the result to find v, and then multiplying by y1(t), you can find the general solution of equation (38). This method simultaneously finds both the second homogeneous solution and a particular solution.
Questions & Answers
QUESTION:
The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y__ + p(t) y_ + q(t) y = g(t), (38) provided one solution y1 of the corresponding homogeneous equation is known. Let y = v(t) y1(t) and show that y satisfies equation (38) if v is a solution of y1(t)v__ + 2y_ 1(t) + p(t) y1(t)v_ = g(t). (39) Equation (39) is a first-order linear differential equation for v_. By solving equation (39) for v_, integrating the result to find v, and then multiplying by y1(t), you can find the general solution of equation (38). This method simultaneously finds both the second homogeneous solution and a particular solution.
ANSWER:Step 1 of 3
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