Solve the following differential equition. Find C1 and C2. #6 Solve the DE. dig -4 og...
Question 2: Differential Equations a) (3 points) Find the general solution to the equation. Use C,C1,C2 ... to denote arbitrary constants as necessary. y"(t) = sin6t + 20e b) (5 points) Solve the following separable differential equation for the given initial condition. y')= (1) = 0 c) (5 points) Solve the following first-order linear differential equation for the given initial condition. y't) + 7y - 3,y(0) - 1 d) (2 points) State the equilibrium solution and whether it is stable...
Find the general solution of the differential equation. Use C1 and C2 to denote any arbitrary constants. 1) y'(t) = y(4t3 + 1) 3) y'(t) = 18t5 – 10t4 + 8 – 2t-2 4) y"(t) = 40e5t + sin(4t)
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...
Solve the system of first-order linear differential equations. (Use C1, C2, and C3 as constants.) Y1 3y2 Y2' 4y1 4y2 + 1473 7y3 = Y3' = 473 (y1(t), y2(t), y(t)) Need Help? Read It Watch It Talk to a Tutor [1/3 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.4.029. Write out the system of first-order linear differential equations represented by the matrix equation y' = Ay. (Use y1, and y2, for yi(t), and yz(t).) [01] Yı' = Y2' =
Question 2 (15 points) Solve the differential equation for the general solution y 6y' 73y 0 y(t) C cos(3t) C2 sin(3t) y(t) = C1 cos(8t) + C2 sin(8t) y(t) cos(8t) +C2e" sin(St) y(t) Ce cos(8t) Cest sin (8t) y (t) = Cleft cos (8t) + C2eft sin (8t) (t)Cest cos(9)Cesin (9t) Previous Page Next Page Page 2 of9
Find the general solution of the following differential equation: (1) ?′′ + 5?′ + 6? = 2????*?^? (2) ?′′ + 2?′ + ? = ? + ?e^(-t). (please solve Question No.7 only) 7. (30 points) Find the general solution of the following differential equation: (1) y" + 5y' + 6y = 2etsint (2) y" + 2y + y=t+te-t 8. (10 points) Use the method of variation of parameters to find a particular solution of y" + y = 1/sin (t),...
(1 point) Solve the following differential equation by variation of parameters. Fully evaluate all integrals. y" +9y sec(3x) a. Find the most general solution to the associated homogeneous differential equation. Use c1 and c2 in your answer to denote arbitrary constants, and enter them as ct and c2. help (formulas) b. Find a particular solution to the nonhomogeneous differential equation y" +9y sec(3x). yp elp (formulaS c. Find the most general solution to the original nonhomogeneous differential equation. Use c...
Consider the differential equation: y' - 5y = -2x – 4. a. Find the general solution to the corresponding homogeneous equation. In your answer, use cı and ca to denote arbitrary constants. Enter ci as c1 and ca as c2. Yc = cle cle5x - + c2 b. Apply the method of undetermined coefficients to find a particular solution. yp er c. Solve the initial value problem corresponding to the initial conditions y(0) = 6 and y(0) = 7. Give...
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
solve the differential equation using the power series For the following differential equations, find 42, 43, 44, 45, 46, and a7 in terms of do and aj and write the answer y(x) = 20 ( sum of terms ) +a1( sum of terms) 2. y" – xy' - y = 0) expanding about xo = 0. 3 -0.