For the following differential equation, show that y1 (t) and y2(t) form a fundamental set of solutions for the given differential equation (check linear independent by computing Wronskian or by definition of linear independent ). Then find a solution to the initial value problems: y" + 2y' + 5y = 0, Y1 (t) = e-tcos2t, y2(t) = e-tsin2t, y(0) = -1, y'(0) = 0

For the following differential equation, show that y1 (t) and y2(t) form a fundamental set of solutions for the given differential equation (check linear independent by computing Wronskian or by definition of linear independent ). Then find a solution to the initial value problems: y" + 2y' + 5y = 0, Y1 (t) = e-tcos2t, y2(t) = e-tsin2t, y(0) = -1, y'(0) = 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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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

Q2
For the following differential equation, show
that y1 (t) and y2 (t) form a fundamental set of
solutions for the given differential equation
(check linear independent by computing
Wronskian or by definition of linear
independent). Then find a solution to the
initial value problems:
y" + 2y' + 5y = 0, yı (t) =
: 0,
e
-tcos2t, y2(t) = =
= e=sin2t, y(0)
-1, y'(0) = 0

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