y" + 100y = sec²(10x)%3D(1) Let C1 and C2 be arbitrary constants. The general solution to the related homogeneousdifferential equation y" + 100y = 0 is the function y, (x) = C1 41(x)+ C2 Y2(x) = C1+C2NOTE: The order in which you enter the answers is important; that is,Cif(x) + C29(x) + C19(x) + C2f(x).(2) The particular solution yp(x) to the differential equation y" + 100y = sec²(10x) is of theform yp(x) = Y1(x) u1(x) + Y½(x) U2(x) where u' (x) =andu, (z) =%3D(3) It follows that u1(x) :and u2(x) =; thus yp(x) =(4) The most general solution to the non-homogeneous differential equationy" + 100y = sec2²(10x) isy = C1+C2

(1) The given equation is, y''+100y=sec210x Solve the homogeneous part y''+100y=0. The auxiliary…

y" + 100y = sec²(10z) (1) Let C1 and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 100y = 0 is the function y, (x) = C1 Y1(x) + C2 Y2(x) = Cı +C2 NO TE: The order in which you enter the answers is important; that is, Cif(x)+ C29(x) # C19(x) + C2f(r). (2) The particular solution yp(x) to the differential equation y" + 100y = sec²(10x) is of the form yp(z) = y1 (x) u, (z) + 2(x) u2(x) where u (z) = and u(x) = (3) It follows that u (2) and u2(x) = ; thus Yp(x) (4) The most general solution to the non-homogeneous differential equation y" + 100y = sec²(10x) is y = C, %3D +C2

y" + 100y = sec²(10z) (1) Let C1 and C2 be arbitrary constants. The general solution to the related homogeneous differential equation y" + 100y = 0 is the function y, (x) = C1 Y1(x) + C2 Y2(x) = Cı +C2 NO TE: The order in which you enter the answers is important; that is, Cif(x)+ C29(x) # C19(x) + C2f(r). (2) The particular solution yp(x) to the differential equation y" + 100y = sec²(10x) is of the form yp(z) = y1 (x) u, (z) + 2(x) u2(x) where u (z) = and u(x) = (3) It follows that u (2) and u2(x) = ; thus Yp(x) (4) The most general solution to the non-homogeneous differential equation y" + 100y = sec²(10x) is y = C, %3D +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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

y" + 100y = sec²(10x)
%3D
(1) Let C1 and C2 be arbitrary constants. The general solution to the related homogeneous
differential equation y" + 100y = 0 is the function y, (x) = C1 41(x)+ C2 Y2(x) = C1
+C2
NOTE: The order in which you enter the answers is important; that is,
Cif(x) + C29(x) + C19(x) + C2f(x).
(2) The particular solution yp(x) to the differential equation y" + 100y = sec²(10x) is of the
form yp(x) = Y1(x) u1(x) + Y½(x) U2(x) where u' (x) =
and
u, (z) =
%3D
(3) It follows that u1(x) :
and u2(x) =
; thus yp(x) =
(4) The most general solution to the non-homogeneous differential equation
y" + 100y = sec2²(10x) is
y = C1
+C2

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