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4. Consider the second-order differential equation (D+1)y=2 cos(x)+sin(x). (a) Use annihilators to reduce the DE to a homogeneous DE. (b) Write the general solution to the DE and circle the terms in the complementary solution. (c) Assuming that y, = Ax cos(x) + Bx sin(x) and y," =(-Ax+2B) cos(x)+(-24-Bx) sin(x), solve for the coefficients A and B in the particular solution. (d) Write the general solution to the DE.

4. Consider the second-order differential equation (D+1)y=2 cos(x)+sin(x). (a) Use annihilators to reduce the DE to a homogeneous DE. (b) Write the general solution to the DE and circle the terms in the complementary solution. (c) Assuming that y, = Ax cos(x) + Bx sin(x) and y," =(-Ax+2B) cos(x)+(-24-Bx) sin(x), solve for the coefficients A and B in the particular solution. (d) Write the general solution to the DE.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Subject : Differential equation

a). 4. Consider the second-order differential equation (D+1)y=2 cos(x)+sin(x). (a) Use annihilators to reduce the DE to a homogeneous DE. (b) Write the general solution to the DE and circle the terms in the complementary solution. (c) Assuming that y, = Ax cos(x) + Bx sin(x) and y, = (-Ax+2B) cos(x)+(-24-Bx) sin(x). solve for the coefficients A and B in the particular solution. (d) Write the general solution to the DE.
Transcribed Image Text:a). 4. Consider the second-order differential equation (D+1)y=2 cos(x)+sin(x). (a) Use annihilators to reduce the DE to a homogeneous DE. (b) Write the general solution to the DE and circle the terms in the complementary solution. (c) Assuming that y, = Ax cos(x) + Bx sin(x) and y, = (-Ax+2B) cos(x)+(-24-Bx) sin(x). solve for the coefficients A and B in the particular solution. (d) Write the general solution to the DE.
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