(a) Consider the differential equation dy dr (i) Solve the equation. (ii) Does the IVP consisting of the equation and the condition y(0) = 1 have a unique solution? If so, determine it. Determine the interval of validity of the solution.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Question
(a) Consider the differential equation
(i) Solve the equation.
(ii) Does the IVP consisting of the equation and the condition y(0) = 1 have a
unique solution? If so, determine it. Determine the interval of validity of the
solution.
(c) Solve the differential equation
(b) Use the substitution u = lny to solve the differential equation
(xy + 2xy In² y + ylny)dx + (2x² Iny+r)dy = 0.
(d) Solve the differential equation
given that y(0) = 1.
dy
dx
(a) Show that the function
x
solves the differential equation
ydx = (ye"-2x)dy.
(e² + y)dx +(2+x+ye³)dy = 0,
Question
BILST
3₁(x) = e-³r
y" - y - 12y = 0
on the interval (-∞0,00).
(b) Hence, or otherwise, use reduction of order to obtain the general solution of the
equation in part (a).
Transcribed Image Text:(a) Consider the differential equation (i) Solve the equation. (ii) Does the IVP consisting of the equation and the condition y(0) = 1 have a unique solution? If so, determine it. Determine the interval of validity of the solution. (c) Solve the differential equation (b) Use the substitution u = lny to solve the differential equation (xy + 2xy In² y + ylny)dx + (2x² Iny+r)dy = 0. (d) Solve the differential equation given that y(0) = 1. dy dx (a) Show that the function x solves the differential equation ydx = (ye"-2x)dy. (e² + y)dx +(2+x+ye³)dy = 0, Question BILST 3₁(x) = e-³r y" - y - 12y = 0 on the interval (-∞0,00). (b) Hence, or otherwise, use reduction of order to obtain the general solution of the equation in part (a).
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