Suppose that yı(t) and y2(t) have continuous second derivatives defined on the entirereal line and their Wronskian is W[y1.y2](t) = et-1. Then ...O... there is not enough information to decide if there exist functions p(t) and q(t),both continuous in the interval (-10,10) such that y1 and y2 are both solutions ofthe differential equation y"+p(t)y'+q(t)y = 0.O... there exist no functions p(t) and q(t), both continuous in the interval(-10,10)such that y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y =0.O... there exist functions p(t) and q(t), both continuous in the interval (-10,10) suchthat y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y = 0.

Suppose that y1(t) and y2(t) have continuous second derivatives defined on the entire real line and their Wronskian is W[y1.Y2](t) = e*-1. Then... %3D ... there is not enough information to decide if there exist functions p(t) and q(t), both continuous in the interval (-10,10) such that y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y = 0. %3D O ... there exist no functions p(t) and q(t), both continuous in the interval (-10,10) such that y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y = 0. %3D there exist functions p(t) and q(t), both continuous in the interval (-10,10) such that y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y = 0. ..

Suppose that y1(t) and y2(t) have continuous second derivatives defined on the entire real line and their Wronskian is W[y1.Y2](t) = e*-1. Then... %3D ... there is not enough information to decide if there exist functions p(t) and q(t), both continuous in the interval (-10,10) such that y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y = 0. %3D O ... there exist no functions p(t) and q(t), both continuous in the interval (-10,10) such that y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y = 0. %3D there exist functions p(t) and q(t), both continuous in the interval (-10,10) such that y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y = 0. ..

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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Concept explainers

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

Suppose that yı(t) and y2(t) have continuous second derivatives defined on the entire
real line and their Wronskian is W[y1.y2](t) = et-1. Then ...
O... there is not enough information to decide if there exist functions p(t) and q(t),
both continuous in the interval (-10,10) such that y1 and y2 are both solutions of
the differential equation y"+p(t)y'+q(t)y = 0.
O... there exist no functions p(t) and q(t), both continuous in the interval(-10,10)
such that y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y =
0.
O... there exist functions p(t) and q(t), both continuous in the interval (-10,10) such
that y1 and y2 are both solutions of the differential equation y"+p(t)y'+q(t)y = 0.

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