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Two solutions to y'' + 4y' - 21y = 0 are y₁=e³, 32 - e-7t a) Find the Wronskian. W- b) Find the solution satisfying the initial conditions y(0) 1, y'(0) - -47

Two solutions to y'' + 4y' - 21y = 0 are y₁=e³, 32 - e-7t a) Find the Wronskian. W- b) Find the solution satisfying the initial conditions y(0) 1, y'(0) - -47

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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Question
Two solutions to y''+ 4y' – 21y = 0 are y = e", y2 = e-74. a) Find the Wronskian. W = b) Find the solution satisfying the initial conditions y(0) = 1, y'(0) = - 47 %3D %3D y =
Transcribed Image Text:Two solutions to y''+ 4y' – 21y = 0 are y = e", y2 = e-74. a) Find the Wronskian. W = b) Find the solution satisfying the initial conditions y(0) = 1, y'(0) = - 47 %3D %3D y =
Two solutions to y'"+ 6y' + 25y = 0 are y1 -3* sin(4t), y2 3t = e * cos(4t). = e a) Find the Wronskian. W = -9e-3t b) Find the solution satisfying the initial conditions y(0) = - 3, y'(0) 11 *( = 3 cos z (t) – 5 sin (t)) x syntax error: you gave an equation, not an expression. syntax e error. Check your variables - you might be using an incorrect one.
Transcribed Image Text:Two solutions to y'"+ 6y' + 25y = 0 are y1 -3* sin(4t), y2 3t = e * cos(4t). = e a) Find the Wronskian. W = -9e-3t b) Find the solution satisfying the initial conditions y(0) = - 3, y'(0) 11 *( = 3 cos z (t) – 5 sin (t)) x syntax error: you gave an equation, not an expression. syntax e error. Check your variables - you might be using an incorrect one.
Expert Solution
Step 1

We know that the Wronskian of two functions y1t and y2t is calculated as:

W=y1ty2ty1t'y2t'

(1)

Consider the given differential equation y"+4y'-21y=0.

The two solution of this differential equations are y1=e3t and y2=e-7t.

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