Use d £f* g(t) dt = g(x) to verify that the indicated function is a solution of the given differential equation. Assume an appropriate interval I of definition of the solution. "x cos(t) dy dx F'(x) = When y = √x = 2x 2x. x d - y = 2x cos(x); y = √x * S* ² cos(t) Thus, in terms of x, dy dx y = √t dt, 1) [x cos(t) dt + *x cos(t) 1) / [ d dt + dt cos(t) √t |-√x/x0= dt
Use d £f* g(t) dt = g(x) to verify that the indicated function is a solution of the given differential equation. Assume an appropriate interval I of definition of the solution. "x cos(t) dy dx F'(x) = When y = √x = 2x 2x. x d - y = 2x cos(x); y = √x * S* ² cos(t) Thus, in terms of x, dy dx y = √t dt, 1) [x cos(t) dt + *x cos(t) 1) / [ d dt + dt cos(t) √t |-√x/x0= dt
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:Use
d
S* g(t) dt = g(x)
to verify that the indicated function is a solution of the given differential equation. Assume an appropriate interval I of definition of the solution.
cos(t)
√x [X COS
dy
dx
F'(x) =
2x
When y = √x
2x
dy
dx
√x [².
- y =
Thus, in terms of x,
dy
dx
dx
- y = 2x cos(x);
[x cos(t)
√t
dt,
[x cos(t)
√t
y=√x
dt +
[x cos(t)
dt +
dt
cos(t)
-√x [*
dt
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