(b). f(x)= cosh (7x)- 2e- using cosh y=+ f(x) = (c). since ex and e* are also put of complementary function Let ..yp(x) = Axe*x+Bex+ce-x+Dxei+Ee-i yp(x) = Aex + +7Axe7+7Bex-7ce-7x '+Dee+x+ Be + = e(A + 7B) + 7Aex-7ce-x-xe+ e*(D-E) Yp"(x) = 7(A+7B)e+7Aex +49Axe7+49ce -fei+ + xe i-}(D- §)e : 4yp"(x)-27y(x)-7yp(x)=+-2e-² substituting perticular equations in above equation and by comparing coefficients on both sides we get the values of constants and perticular equation is as follows: Yp(x)=+²x+eix (e). y(0) y'(0) = 0 -2e-² (d). The general solution is y(x) = e+exx+eix+c₁e + c₂e²x = 1,513 756 1,513 756 C₁+C₂ + 756 = 241 - +7c₂+ 3,132 44,089 01= 22,707 = =0 1,513 756 -7x 1,325 and C2 = 22,707
(b). f(x)= cosh (7x)- 2e- using cosh y=+ f(x) = (c). since ex and e* are also put of complementary function Let ..yp(x) = Axe*x+Bex+ce-x+Dxei+Ee-i yp(x) = Aex + +7Axe7+7Bex-7ce-7x '+Dee+x+ Be + = e(A + 7B) + 7Aex-7ce-x-xe+ e*(D-E) Yp"(x) = 7(A+7B)e+7Aex +49Axe7+49ce -fei+ + xe i-}(D- §)e : 4yp"(x)-27y(x)-7yp(x)=+-2e-² substituting perticular equations in above equation and by comparing coefficients on both sides we get the values of constants and perticular equation is as follows: Yp(x)=+²x+eix (e). y(0) y'(0) = 0 -2e-² (d). The general solution is y(x) = e+exx+eix+c₁e + c₂e²x = 1,513 756 1,513 756 C₁+C₂ + 756 = 241 - +7c₂+ 3,132 44,089 01= 22,707 = =0 1,513 756 -7x 1,325 and C2 = 22,707
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:(b).
f(x)= cosh (7x) - 2e-²
using cosh y =
f(x) = **+- 2e-
(c).
since ex and e* are also put of complementary function
Let
..yp(x) =
yp(x) = Ae* + +7Axe7x + 7Be¹x7ce-7x +Dei ex± e
= ex (A + 7B) + 7Ae¹xx-7ce-x-xe+ e* (D- )
Yp"(x) = 7(A + 7B)ex + 7Ae7x +49Axe7x +49ce-7x De+Pxe - (D-)e
4yp"(x)-27y(x)-7yp(x)=+-2e-*
substituting perticular equations in above equation
and by comparing coefficients on both sides
we get the values of constants and perticular equation is as follows:
Yp(x) = 6 +x+eix
= Axex +Bex + ce 7x +Dxe + Ee-
(d).
The general solution is
y(x) = e-76+exx + ex+c₁e + c₂e7x
(e).
1,513
y(0) = 756¹
y'(0) = 0
1,513
756
C₁+C₂ + 756 =
-4+7c₂ +
241
3,132
C1 =
44,089
22,707
and
=
=0
C₂ =
1,513
756
1,325
22,707
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