Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y"8y' + 25y = 0; y = e4x cos 3x When y = e4x cos 3x, y' = 4x -3esin 3x + 4ecos 3x X -24e4xsin 3x + 7e4x cos 3x x Thus, in terms of x, y" - 8y' + 25y = 7e4x cos 3x - 24e4xsin 3x 0 X + 25 e4x cos 3x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
y"8y' + 25y = 0;
y = e4x cos 3x
When y = e4x cos 3x,
y' =
y" =
4x
-3esin 3x + 4e cos 3x
4x
X
-24e4xsin 3x + 7e¹xcos 3x
Thus, in terms of x,
y"8y' + 25y = 7ecos 3x -
4x
0
X
– 24e4xsin 3x
X
+ 25 e4x cos 3x
Transcribed Image Text:Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y"8y' + 25y = 0; y = e4x cos 3x When y = e4x cos 3x, y' = y" = 4x -3esin 3x + 4e cos 3x 4x X -24e4xsin 3x + 7e¹xcos 3x Thus, in terms of x, y"8y' + 25y = 7ecos 3x - 4x 0 X – 24e4xsin 3x X + 25 e4x cos 3x
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Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
y"8y' + 25y = 0;
y = e4x cos 3x
When y = e4x cos 3x,
y' =
y" =
4x
-3esin 3x + 4e cos 3x
4x
X
-24e4xsin 3x + 7e¹xcos 3x
Thus, in terms of x,
y"8y' + 25y = 7ecos 3x -
4x
0
X
– 24e4xsin 3x
X
+ 25 e4x cos 3x
Transcribed Image Text:Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y"8y' + 25y = 0; y = e4x cos 3x When y = e4x cos 3x, y' = y" = 4x -3esin 3x + 4e cos 3x 4x X -24e4xsin 3x + 7e¹xcos 3x Thus, in terms of x, y"8y' + 25y = 7ecos 3x - 4x 0 X – 24e4xsin 3x X + 25 e4x cos 3x
Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
y" - 8y' + 25y = 0; y = e4x cos 3x
When y = e4x cos 3x,
y' =
y" =
4x
4ecos 3x - 3e sin 3x
7e¹xcos 3x - 24e4xsin 3x
=
X
Thus, in terms of x,
y" - 8y' + 25y = 7e4x cos 3x - 24e4xsin 3x -
0
X
c − 32e¹xcos 3x + 24e4x sin 3x
X
+ 25 e¹x cos 3x
Transcribed Image Text:Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y" - 8y' + 25y = 0; y = e4x cos 3x When y = e4x cos 3x, y' = y" = 4x 4ecos 3x - 3e sin 3x 7e¹xcos 3x - 24e4xsin 3x = X Thus, in terms of x, y" - 8y' + 25y = 7e4x cos 3x - 24e4xsin 3x - 0 X c − 32e¹xcos 3x + 24e4x sin 3x X + 25 e¹x cos 3x
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