Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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 +

Calculus For The Life Sciences
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
See similar textbooks
icon
Related questions
Question
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 +
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 +
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS