Q1) L-1 a) cosht -1 b) 1 - cosht c) (cosh2t - 1) d)/(1-cosh2t) Q2) The general solution of y"" + 2y" -y' - 2y = 0, is: a) y(x) = c₂e²x + c₂e-* + c3e* c) y(x) = c₁e²x + c₂ex b) y(x) = c₂e-2x + c₂e-* d) y(x) = c₂e-2x + ₂x + c₂e-* Q3) Evaluate L (e-2t sin4t): 4 s+2 a) 5+2 s²+8s+20 S²+45+20 d) S²+45+20 s²+85+20 Q4) If the power series method was used to solve the following ODE. (x-0.5)y"-5 y' + (x² - 1) y=0, x= 0. Then the interval of convergence, is: a) (²) b) (-1,1) c) (0,00) Q5) fest dt = е b) 0 c)=² d) ∞ . y Q6) If you know that the radius of convergent of the series method for the ODE y"+y' + = 0, xo = 2 is 5. Find the value for b. (b < 0): (a) -5 x-b (b)-3 (c)-2 d) -8 Q7) L(y") = - a) s²L(y(x)) + sy(0) - y'(0) b) s² L(y(x)) + sy(0) + y'(0) d) s²L(y(x)) - sy(0) + y'(0) c) s²L(y(x)) - sy(0) - y'(0) Q8) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant coefficients are 0,0,0,2+5i,2-5i, then the general solutiom of this ODE, is: a) C₁ + C₂x + C3x² + e²x [Acos(x) + Bsin(x)] b) C₁+C₂x + C3x² +e5x[Acos (2x) + Bsin(2x)] c) C₁x + ₂x² + C3x³ + ex[Acos (5x) + Bsin(5x)] d) C₁ + C₂x + C3x² + e²x [Acos (5x) + Bsin(5x)] Q9) The linear form of nonlinear ODE y' - 2y = 2y, is: a) u' + 6u = -6 b) u' - 6u = -6 c) u' - 6u = 6 d) u' + 6u = 6 Q10) The singular point (s) of (x + 1) y' + x²y = 0, is (are): b) 0,-1 a) 0,1 c) 0 d)-1
Q1) L-1 a) cosht -1 b) 1 - cosht c) (cosh2t - 1) d)/(1-cosh2t) Q2) The general solution of y"" + 2y" -y' - 2y = 0, is: a) y(x) = c₂e²x + c₂e-* + c3e* c) y(x) = c₁e²x + c₂ex b) y(x) = c₂e-2x + c₂e-* d) y(x) = c₂e-2x + ₂x + c₂e-* Q3) Evaluate L (e-2t sin4t): 4 s+2 a) 5+2 s²+8s+20 S²+45+20 d) S²+45+20 s²+85+20 Q4) If the power series method was used to solve the following ODE. (x-0.5)y"-5 y' + (x² - 1) y=0, x= 0. Then the interval of convergence, is: a) (²) b) (-1,1) c) (0,00) Q5) fest dt = е b) 0 c)=² d) ∞ . y Q6) If you know that the radius of convergent of the series method for the ODE y"+y' + = 0, xo = 2 is 5. Find the value for b. (b < 0): (a) -5 x-b (b)-3 (c)-2 d) -8 Q7) L(y") = - a) s²L(y(x)) + sy(0) - y'(0) b) s² L(y(x)) + sy(0) + y'(0) d) s²L(y(x)) - sy(0) + y'(0) c) s²L(y(x)) - sy(0) - y'(0) Q8) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant coefficients are 0,0,0,2+5i,2-5i, then the general solutiom of this ODE, is: a) C₁ + C₂x + C3x² + e²x [Acos(x) + Bsin(x)] b) C₁+C₂x + C3x² +e5x[Acos (2x) + Bsin(2x)] c) C₁x + ₂x² + C3x³ + ex[Acos (5x) + Bsin(5x)] d) C₁ + C₂x + C3x² + e²x [Acos (5x) + Bsin(5x)] Q9) The linear form of nonlinear ODE y' - 2y = 2y, is: a) u' + 6u = -6 b) u' - 6u = -6 c) u' - 6u = 6 d) u' + 6u = 6 Q10) The singular point (s) of (x + 1) y' + x²y = 0, is (are): b) 0,-1 a) 0,1 c) 0 d)-1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.10: Partial Fractions
Problem 17E
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please solve question 5 differential equations
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