Find the general solution of the differential equations: (a) dx dt (b) x2 dy dx x² (1+t) + xy = x² e for x > 0
Find the general solution of the differential equations: (a) dx dt (b) x2 dy dx x² (1+t) + xy = x² e for x > 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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Question
Transcribed Image Text:Find the general solution of the differential equations:
dx
(a) = x²(1 +t)
dt
dy
dx
(b) x².
+ xy = x²e for x > 0
Find the solution to the initial value problem. Write your answer in the form y = f (x) for some
function f.
dy = y³ + 2xy³, y(0)
dx
= -1
—
Use Euler's method with four steps of size h
=
0.1 to find an approximation to the solution of
y' = 2t - y if y(0) = 0. What is your approximate value of y(0.4)?
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