Consider the following second order differential equation: d²y dx dx² +5x + 16xy = 3x² with y(0) = 6 and y'(0) = 10 dy If we let u = y and v=y' then as an AUTONOMOUS first order system, the second order differential equation is correctly expressed as: O A du dx O B da dt da dt O D du d.r =y', u(0) = 6, = 1, x(0) = 1, = 1, x(to) = 0, = v, u(0) = 6, OE dr dt F None of these. = 1, x(to) = 0, dv dr du d.x du dt du dr du dt = 3x² - 16xy - 5xy', v(0) = 10. dv = v, u(0) = 6, = 3x² - 16xu - 5xv, v(0) = 10 dx =v, u(to) = 6, dv dt = v, u(to) = 6, = 3x² - 16xu - 5xv, v(0) = 10. = 3x² 16xv - 5xu, v(to) = 10 dv dt = 3x² - 16xu - 5xv, v(to) = 10.
Consider the following second order differential equation: d²y dx dx² +5x + 16xy = 3x² with y(0) = 6 and y'(0) = 10 dy If we let u = y and v=y' then as an AUTONOMOUS first order system, the second order differential equation is correctly expressed as: O A du dx O B da dt da dt O D du d.r =y', u(0) = 6, = 1, x(0) = 1, = 1, x(to) = 0, = v, u(0) = 6, OE dr dt F None of these. = 1, x(to) = 0, dv dr du d.x du dt du dr du dt = 3x² - 16xy - 5xy', v(0) = 10. dv = v, u(0) = 6, = 3x² - 16xu - 5xv, v(0) = 10 dx =v, u(to) = 6, dv dt = v, u(to) = 6, = 3x² - 16xu - 5xv, v(0) = 10. = 3x² 16xv - 5xu, v(to) = 10 dv dt = 3x² - 16xu - 5xv, v(to) = 10.
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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Transcribed Image Text:Consider the following second order differential equation:
d²y d.x
dx²
+52 + 16xy = 3x² with y(0) = 6 and y' (0) = 10
dy
If we let u = y and v = y' then as an AUTONOMOUS first order system, the second order differential equation is correctly expressed as:
O A du
dv
= y', u(0) = 6, = 3x² - 16xy - 5xy', v(0) = 10.
d.x
d.x
O B
d.x
dt
O c dx
dt
O
D du
da
=
1, x(0) = 1,
= 1, x (to) = 0,
=
o, u(0)
O E dx
dt
F None of these.
=
6,
1, x(to) = 0,
du
dv
= v, u(0) = 6, = 3x² - 16xu - 5xv, v(0) = 10
dx
dx
du
dt
dv
dx
du
dt
=v, u(to) = 6,
= 3x² - 16xu
=v, u(to) = 6,
dv
dt
= 3x² 16xv 5xu, v(to) = 10.
5xv, v(0) 10.
dv
dt
= 3x² - 16xu - 5xv, v(to) = 10.
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