Consider the nonhomogeneous linear equation y"- y= g(t) where g is a continuous function. Let y,() =1(t)u, (t) +y2(t)uz(t) be a particular solution of the given equation, where {yı(t), y2(t)} is a fundamental set of solutions for the corresponding homogeneous equation. ) Find the equations satisfied by u (t) and u (1). ) Determine y, for g(t) = e. O a i) u (t) = -g(t), u(t) - 9(t)e t, i) y, = (t – 1)e' Ob. i) 4 (t) = 9(t)e , (t) = g(t), ii) y, = (1 – t)e' Oc i) u (t) = 9(t), (t) = g(t)(1 – e *), üi) y, = (-2 + t)e O d. i) u (t) = g(t)(1 – e'), ½(t) = 9(t)e , ü) y, = (t + 2)e'

Consider the nonhomogeneous linear equation y"- y= g(t) where g is a continuous function. Let y,() =1(t)u, (t) +y2(t)uz(t) be a particular solution of the given equation, where {yı(t), y2(t)} is a fundamental set of solutions for the corresponding homogeneous equation. ) Find the equations satisfied by u (t) and u (1). ) Determine y, for g(t) = e. O a i) u (t) = -g(t), u(t) - 9(t)e t, i) y, = (t – 1)e' Ob. i) 4 (t) = 9(t)e , (t) = g(t), ii) y, = (1 – t)e' Oc i) u (t) = 9(t), (t) = g(t)(1 – e *), üi) y, = (-2 + t)e O d. i) u (t) = g(t)(1 – e'), ½(t) = 9(t)e , ü) y, = (t + 2)e'

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Consider the nonhomogeneous linear equation y"- y= g(t) wheregis a continuous function. Let y,(t) = y1(t)u1 (t) + y2(t)u2(t) be a particular solution of the given equation, where {y1(t), y2(t)} is a fundamental set
of solutions for the corresponding homogeneous equation. i) Find the equations satisfied by u (t) and u, (t). ii) Determine y, for g(t) = e.
O a. i) uf (t) = -9(t), u,(t) = g(t)e ', üi) y, = (t – 1)e'
O b. i) uf (t) = g(t)e , u (t) = g(t), i) y, = (1 – t)e
O a i) u; (t) = g(t), u(t)=g(t)(1-e *), i) yp = (-2+t)e'
O d. î) u (t) = g(t)(1 – e'), u½(t) = g(t)e ', ii) yp = (t + 2)e'

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