Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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please solve question19 differential equations

.Q11) The general solution of y" - 4y' +9y = 0, is: a) y(t) = c₂e2t cos(5 t) + c₂e2t sin (5 t) c)y(t) = c₂e2t cos(√5 t) + c₂e²t sin (√5 t) b)y(t) = cet cos(√5 t) + c₂e²sin (√5t) d) y(t) = ce cos(5 t) + c₂esin (5 t) 012) The formula of the particular solution yp of y(4) + 4y" = 3 sin(2t) - 5cos2t, is: a) yp= Asin(t) + Bcos(t) c) yp Asin(2t) + Bcos(2t) b) yp = Atsin(t) + Btcos(t) d) yp = Atsin(2t) + Btcos (2t)] Q13) The general solution for y' = 6y²x, is: a) = 3x² + c b) = x² + c c) == 3x² + c d) == x² + c Q14) The solution of y" + y'= 0 by using power series method, is: a) y(x) = ao + a₁(1) c) y(x) = ao + a₁(x- x²x²x² 21 31 x²x² ..) x² b) y(x) = ao + a₂ (1+ 21 d)y(x) = ao + a₂(x+: Q15) Given that y₁ (t) = t¹ is solution for 2t²y" + ty' - 3y = 0,t> 0, then y₂ (t) is: 41 51 x5 x¹ 314151) x² =+= a) t b) tz Q16) L-¹ (5-3)²+25) d) ti c) tz etsinst 5 = a) e-3t sin3t eatsinst b) est sin3t 5 C) d) Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t): a) (s+2)²+16 25² +18 b) (5-2)2+16 c) 2s²+18 (5+2)2+16 25+18 (S-2)2+16 25² +18 Q18) Combine the following power series expressions into a single power series. En 1(n+1)(x-2)n-1 + Σon(x - 2)" a) Eno(2n + 1)(x)" b) En-o(2n + 2)(x)" c) Eno(2n + 2)(x - 2)" d) (2n + 1)(x-2)" Q19) The general solution of 2x²y" + 3xy' - 15y = 0, is: a) y(x) = C₁x² + ₂x³ b) y(x) = C₁x + ₂x-3 c) y(x) = ₂x² + ₂x-3 d) y(x) = x² + ₂x³ Q20) The form of a particular solution of y"-4y' - 12y = sin(2t), is: a) yp (t) = A sin(2t) b) y(t) = A cos(t) . c) y(t) = A cos (2t) + B sin(2t) d) y(t) = A cos(t) + B sin(t) Q21) One of the following is correct for functions the f(x) = 1, g(x) = x³ and h(x) = ln(x): a) f(x), g(x) and h(x) are linearly dependent c) W (f(x), g(x), h(x)) = 0 b) f(x), g(x) and h(x) are linearly independe d) W (f(x), g(x), h(x)) = 9 = is: (3s+2)(S-2) S' Q22) The inverse Laplace transform of H(s) b) f(t)= e+e- a) f(t) ==e¹+¹e²t -3 -2 8 -2, c) f(t) = ¹ + 1 e e-2t d)f (t) ==³e²¹ +²e²t Q23) The kernel of the Laplace transform of f(t), t > 0, is: b) e-t c) e-st d) e-s a) e Q24) The Integrating factor which make (3x2y + 2xy + y³) dx + (x² + y²)dy = 0 exact, is: a) e-3x b) ex d) e 3x b) -2sinhnt c)-2cosnt d) -2sinnt Q25) L-1 -2s S²+T² a) -2coshnt = ·+...)
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Transcribed Image Text:.Q11) The general solution of y" - 4y' +9y = 0, is: a) y(t) = c₂e2t cos(5 t) + c₂e2t sin (5 t) c)y(t) = c₂e2t cos(√5 t) + c₂e²t sin (√5 t) b)y(t) = cet cos(√5 t) + c₂e²sin (√5t) d) y(t) = ce cos(5 t) + c₂esin (5 t) 012) The formula of the particular solution yp of y(4) + 4y" = 3 sin(2t) - 5cos2t, is: a) yp= Asin(t) + Bcos(t) c) yp Asin(2t) + Bcos(2t) b) yp = Atsin(t) + Btcos(t) d) yp = Atsin(2t) + Btcos (2t)] Q13) The general solution for y' = 6y²x, is: a) = 3x² + c b) = x² + c c) == 3x² + c d) == x² + c Q14) The solution of y" + y'= 0 by using power series method, is: a) y(x) = ao + a₁(1) c) y(x) = ao + a₁(x- x²x²x² 21 31 x²x² ..) x² b) y(x) = ao + a₂ (1+ 21 d)y(x) = ao + a₂(x+: Q15) Given that y₁ (t) = t¹ is solution for 2t²y" + ty' - 3y = 0,t> 0, then y₂ (t) is: 41 51 x5 x¹ 314151) x² =+= a) t b) tz Q16) L-¹ (5-3)²+25) d) ti c) tz etsinst 5 = a) e-3t sin3t eatsinst b) est sin3t 5 C) d) Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t): a) (s+2)²+16 25² +18 b) (5-2)2+16 c) 2s²+18 (5+2)2+16 25+18 (S-2)2+16 25² +18 Q18) Combine the following power series expressions into a single power series. En 1(n+1)(x-2)n-1 + Σon(x - 2)" a) Eno(2n + 1)(x)" b) En-o(2n + 2)(x)" c) Eno(2n + 2)(x - 2)" d) (2n + 1)(x-2)" Q19) The general solution of 2x²y" + 3xy' - 15y = 0, is: a) y(x) = C₁x² + ₂x³ b) y(x) = C₁x + ₂x-3 c) y(x) = ₂x² + ₂x-3 d) y(x) = x² + ₂x³ Q20) The form of a particular solution of y"-4y' - 12y = sin(2t), is: a) yp (t) = A sin(2t) b) y(t) = A cos(t) . c) y(t) = A cos (2t) + B sin(2t) d) y(t) = A cos(t) + B sin(t) Q21) One of the following is correct for functions the f(x) = 1, g(x) = x³ and h(x) = ln(x): a) f(x), g(x) and h(x) are linearly dependent c) W (f(x), g(x), h(x)) = 0 b) f(x), g(x) and h(x) are linearly independe d) W (f(x), g(x), h(x)) = 9 = is: (3s+2)(S-2) S' Q22) The inverse Laplace transform of H(s) b) f(t)= e+e- a) f(t) ==e¹+¹e²t -3 -2 8 -2, c) f(t) = ¹ + 1 e e-2t d)f (t) ==³e²¹ +²e²t Q23) The kernel of the Laplace transform of f(t), t > 0, is: b) e-t c) e-st d) e-s a) e Q24) The Integrating factor which make (3x2y + 2xy + y³) dx + (x² + y²)dy = 0 exact, is: a) e-3x b) ex d) e 3x b) -2sinhnt c)-2cosnt d) -2sinnt Q25) L-1 -2s S²+T² a) -2coshnt = ·+...)
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