SOLVE Q8 Q1) One of the following is correct for functions the f(x) = 1, g(x)= x³ and h(x)Ma) f(x), g(x) and h(x) are linearly dependentc) W (f(x), g(x), h(x)) = 0b) f(x), g(x) and h(x) are linearly independentd) W(f(x), g(x), h(x)) = 9Q2) L-1-2s2+3Ha) -2coshntb)-2sinhntc)-2cosntd)-2sinntQ3) The Integrating factor which make (3x2y + 2xy + y³)dx + (x² + y²)dy = 0 exact, is:a) e-3xb) ei*d) e³xQ4) The linear form of nonlinear ODE y' - 2y = 2y, is:a) u' + 6u = -6b) u' - 6u = -6c) u'-6u = 6d) u' + 6u = 6Q5) The general solution of 2x2y" + 3xy'-15y = 0, is:a) y(x) = ₂x² + ₂x³b) y(x) = ₂x + ₂x-3c) y(x) = c₁x² + ₂x-3d) y(x) = c₁x + ₂x³Q6) Evaluate L (2 e-2 sin4t -0.5 cos3t):8Sa)(s+2)² +16b)c) (8+2)² +16 23²418(5-2)2+1625² +182s² +18(s-2)² +16Q7) The general solution of y"-4y' +9y = 0, is:a) y(t)=ce²t cos(5 t) + c₂e²tsin (5 t)c)y(t) = cet cos(√5 t) + c₂e²t sin (√5 t)Q8) The inverse Laplace transform of H(s):b)y(t) = ce cos(√5 t) + c₂e¹sin (√5t)d) y(t) = ce cos(5 t) + cesin (5 t)1=is:.(35+2)(5-2)a) f(t) ==e+e²tb) f(t) ==e.8c) f(t) ==e+e-2td)f(t) ==e.+²e²tQ9) The solution of y" + y'= 0 by using power series method, is:a) y(x) = ao + a₁ (1-11b) y(x) = a + a₁(1+213141St21c) y(x) = a₁ + a₁(x-+d)y(x) = a + a₂(x + ==51-e-2t12s² +18+ +ii414151+++ ...)

Some of the Properties of Laplace transformation…

a) y(t)=ce²t cos(5 t) + c₂e² sin c)y(t)=ce²t cos(√5 t) + c₂et sin (√5 t) Q8) The inverse Laplace transform of H(s) d) y(t) = ce cos(5 t) + c 1 is: F T (35+2)(5-2) 2t a) f(t)=e+ b) f(t) ==e+ 8 1-2t +²e²t d)f(t)= c) f(t) ==e+e om The solution of y" + y'= 0 by using power series method, is: -2t h) y(x) = a + a₂ (1

a) y(t)=ce²t cos(5 t) + c₂e² sin c)y(t)=ce²t cos(√5 t) + c₂et sin (√5 t) Q8) The inverse Laplace transform of H(s) d) y(t) = ce cos(5 t) + c 1 is: F T (35+2)(5-2) 2t a) f(t)=e+ b) f(t) ==e+ 8 1-2t +²e²t d)f(t)= c) f(t) ==e+e om The solution of y" + y'= 0 by using power series method, is: -2t h) y(x) = a + a₂ (1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 92E

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