In this problem you will solve the non-homogeneous differential equation on the interval -π/6 < x < π/6. (1) Let C₁ and C₂ be arbitrary constants. The general solution of the related homogeneous differential equation y' +9y = 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" +9y = sec²(3x) is of the form yp(x) = y₁(x) u₁(x) + y2(x) u2(x) where u₁(x) = and u₂(x) (3) It follows that u1(r) thus yp(x): = y"' +9y = sec² (3x) = and u₂(x) = (4) Therefore, on the interval (-π/6, π/6), the most general solution of the non-homogeneous differential equation y" +9y = = sec² (3x) is y = C₁ +C₂ +
In this problem you will solve the non-homogeneous differential equation on the interval -π/6 < x < π/6. (1) Let C₁ and C₂ be arbitrary constants. The general solution of the related homogeneous differential equation y' +9y = 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" +9y = sec²(3x) is of the form yp(x) = y₁(x) u₁(x) + y2(x) u2(x) where u₁(x) = and u₂(x) (3) It follows that u1(r) thus yp(x): = y"' +9y = sec² (3x) = and u₂(x) = (4) Therefore, on the interval (-π/6, π/6), the most general solution of the non-homogeneous differential equation y" +9y = = sec² (3x) is y = C₁ +C₂ +
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:In this problem you will solve the non-homogeneous differential equation
on the interval -π/6 < x < π/6.
(1) Let C₁ and C₂ be arbitrary constants. The general solution of the related homogeneous differential equation y' +9y = 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" +9y = sec²(3x) is of the form yp(x) = y₁(x) u₁(x) + y2(x) u2(x)
where u₁(x) =
and u₂(x)
(3) It follows that
u1(r)
thus yp(x):
=
y"' +9y = sec² (3x)
=
and u₂(x) =
(4) Therefore, on the interval (-π/6, π/6), the most general solution of the non-homogeneous differential equation y" +9y = = sec² (3x)
is y = C₁
+C₂
+
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