(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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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