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Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 34CR
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In this problem you will solve the non-homogeneous differential equation
on the interval -π/14 < x < π/14.
(1) Let C₁ and C₂ be arbitrary constants. The general solution of the related homogeneous differential equation y +49y = 0 is the function
yh(x) = C₁ y₁(x) + C₂ y2(x) = C₁
+C₂
(2) The particular solution y(x) to the differential equation y" + 49y = sec² (7x) is of the form yp(x) = y₁(x) u₁(x) + y2(x) u2(x)
where u₁(x)
and u₂(x) =
=
(3) It follows that
un(r)
thus yp(x)
=
=
=
y" +49y = sec² (7x)
and u₂(x) =
(4) Therefore, on the interval (—π/14, π/14), the most general solution of the non-homogeneous differential equation y" +49y = sec²(7x)
is y = C₁
+C₂
+
Transcribed Image Text:In this problem you will solve the non-homogeneous differential equation on the interval -π/14 < x < π/14. (1) Let C₁ and C₂ be arbitrary constants. The general solution of the related homogeneous differential equation y +49y = 0 is the function yh(x) = C₁ y₁(x) + C₂ y2(x) = C₁ +C₂ (2) The particular solution y(x) to the differential equation y" + 49y = sec² (7x) is of the form yp(x) = y₁(x) u₁(x) + y2(x) u2(x) where u₁(x) and u₂(x) = = (3) It follows that un(r) thus yp(x) = = = y" +49y = sec² (7x) and u₂(x) = (4) Therefore, on the interval (—π/14, π/14), the most general solution of the non-homogeneous differential equation y" +49y = sec²(7x) is y = C₁ +C₂ +
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,