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Solve the DE, given x > 0. 2 dy dar +y = = 3 In x с Oy= (In x - 2) + 2 None of these Oy= (In x - 2) +C Both of them
2. a) Solve the differential equation: 2²/" - 6xy' = 27 6 Oy=4 +6226 + Ins 6 36 Oy=c+ c2 26 76 36 + In 3 6 6 27 Oy=4+ c227 + In 7 ...7 49 Oy=q+cqz? 27 In 2 49 +7 None of the above b) Solve the differential equation: 9z+y" + 9xy' +25y = 0 Oy= cos(5 ln /3) + sin(5 In 3/3) Oy=425 +2.23 Oy=C1 cos(52/3) + 2 sin(5x/3) y=4125 + c2205 in None of the above...
If the functions y = 2 and y = xe” are linearly independent solutions of the non-homogeneous second-order linear differential equation with variable coefficients z? yll – x(x + 2)y! + (x + 2)y=2, its general solution is given by O = C1z? +Cze” – Oy=C12 + Cexe" – 3:2 Oy=C1 + Cyce + 2? Oy=Cjx+Cazé - 23 None of them
Question 6 3 pts If the functions y = x and y = xe are linearly independent solutions of the non-homogeneous second-order linear differential equation with variable coefficients xʻyll – x(x + 2)yı + (x + 2)y = x3, its general solution is given by Oy=C1x + C2x² cm – 23 Oy=C1x2 + C2xell – 23 None of them y = C1+C2ce® +22 O 9= C1z+C2cef - 22
Use Laplace Transform to identify Y(s) of the DE: y"-y'-by = 0, given y(0) = 1, y'(O) = 2. O None of them Both are correct. Y(s) = 4 5(8-3) + 5(8+2) OY (s) = 8+1 (5-3)(8+2)
1. Solve by making a substitution to reduce the given second order De to a first order DE. 1. x? y" + 2xy' - 1 = 0, x>0 (ans. y = Cix-1 + 2 + In x) 2. y" + y(y')} = 0 (ans. 1/3 y3 - 2c1y + C2 = 2x) 3. y'y” = 2, y(0) = 1, y'(0) = 2 (ans. y = 4/3 (x + 1)3/2 - 1/3)
If the functions y = x and y = xe" are linearly independent solutions of the non-homogeneous second-order linear differential equation with variable coefficients z_ yll – x(x + 2)y + (x+2)y=r, its general solution is given by Oy=C1 + C2xe" + x2 O y=C1x + C2xe - 22 None of them O y=C12 + C2z²er - 23 Oy=C12? + Cymet – x3
Question 1 5 pts What is the order of the DE? Is the DE linear or nonlinear? 3 54' - (tan x)y= Vx+ +1 (7) 5.22 3rd order; nonlinear 2nd order; nonlinear 2nd order; linear 3rd order; linear LUCSLIUI 5 pts Is the function y=2e-32 - 4e5x a solution to the DE? Y' - 2y - 15y = 0 O No O Yes Question 3 5 pts Solve the separable DE. dy 3.cy + 2y - 15x - 10 dac...
Question 1 5 pts Determine the Laplace transform of the given function f(t) = teu cos 4t OF(s) = (8-4)2-16 [18-4)2+16) None of them OF(8) (8-4)2-16 [(-4)2+4)* (8-4)2-4 [(8-4)2 +16] OF(s) Question 2 5 pts The general solution for the differential equation with x as the independent variable to y(4) - y" – 9y' +11y +6y=is_(Hint: y(x) = e(1- 2) is a solution.] 32 + Cle2 Oy(x) = cze(1+x2)x + cze(1-12x + c3 e3x + c4e-2x y(x) = cjell-v2)x +...
Solve the following differential equition. Find C1 and C2. #6 Solve the DE. dig -4 og sy=0 761=0,341)=9 -9 4²-46-5-0 5 y=56.87 Get (m-57 (m+1)=0 y (11 =9=50,8 ce w=5, 1 %= Cetç 2 (1)=o= C, e te est cel 9=50, et le - How do you find G & C₂ ?