In this exercise you will solve the initial value problem "14y +49y= (1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 14y +49y=0 is the function ya(z) = C₁ y1(z) + C₂ 32(z) = C₁ +C₂ e-72 1+z2 y(0) = 10, 3/(0) = 6. NOTE: The order in which you enter the answers is important; that is, C₁ f(x) + C₂g(z) Cig(x) + C₂f(x). (2) The particular solution yp(z) to the differential equation y + 14y/+49y=1 is of the form yp(x) = ₁(z) u₁(x) + 2(x) 1₂(z) where u₁(z) = y= (3) The most general solution to the non-homogeneous differential equation "14y/+49y=is + dt+ dt and u₂(x) =
In this exercise you will solve the initial value problem "14y +49y= (1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 14y +49y=0 is the function ya(z) = C₁ y1(z) + C₂ 32(z) = C₁ +C₂ e-72 1+z2 y(0) = 10, 3/(0) = 6. NOTE: The order in which you enter the answers is important; that is, C₁ f(x) + C₂g(z) Cig(x) + C₂f(x). (2) The particular solution yp(z) to the differential equation y + 14y/+49y=1 is of the form yp(x) = ₁(z) u₁(x) + 2(x) 1₂(z) where u₁(z) = y= (3) The most general solution to the non-homogeneous differential equation "14y/+49y=is + dt+ dt and u₂(x) =
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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Question
Solve all threee parts.
only HANDWRITTEN answer needed ( NOT TYPED)
Transcribed Image Text:In this exercise you will solve the initial value problem
e
-71
=
(3) The most general solution to the non-homogeneous differential equation y" - 14y + 49y=
y" - 14y' + 49y=
y(0) = 10, y'(0) = 6.
(1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 14y' +49y = 0 is the function yh(x) = C₁ y₁(x) + C2 y2(x) = C₁
+C₂
1+x²¹
NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C29(x) + C19(x) + C₂f(x).
(2) The particular solution yp(z) to the differential equation y" + 14y +49y=1 is of the form yp(x) = y₁(x) u₁(x) + y2(x) u₂(r) where u₁(x) =
is
dt +
dt
and u₂(x) =
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