Problem 1. (20 points) Find the general solution to the following differential equations. (a) ty" +...
Solve the Differential problem? Find the general solution of the following system of differential Equations. Show a" the steps of your work. y = 6 yı - y2 V2 = 5y +442 Page 1 a + (hp)
non-homo 2nd order linear equations 1. Find the general solution for each of the following differential equations (10 points each): (a) (b) (e) y" – 2y! - 3y = 3e2x y" — y' – 2y = -2.3 + 4.2? y" + y’ – 67 = 1234 + 12e-2x y" – 2y' – 3y = 3.ce-1 y" + 2y' + y = 2e- (Hint: you'll use Rule 7. at least once) (e 2. Find the solution to the following differential equation...
Problem 2. (10pts.) Find the general solution to the system of differential equations y' = 2 - 2 z' = 5y + 42
FIND THE GENERAL SOLUTION Need ALL 4. Differential Equations class Problem 1 Find the general solution 1. r(t) = (-2)=(0) o 1 1 2. x'(t) = (1 0 1 ) r(t) 1 1 0 3. x'(t) = 1) 2(0) 4. x'(t) = ( = (* 3+:) <60)
Problem 3. Find the general solution of the following first order differential equations. If an initial condition is given find the specific solution. a) xy'y - exy. Suggestion: Set u xy c) y, + 2xy2-0 , y(2)-1
Undetermined Coefficients: Find the general solution for the differential equations. Find the general solution for the following differential equations. (1) y' - y" – 4y' + 4y = 5 - e* + e-* (2) y" + 2y' + y = x²e- (3) y" - 4y' + 8y = x3; y(0) = 2, y'(0) = 4
5. Find the general solution of the following differential equations: (a) 6"-5y y 0 (b) 4y"+12y9y 0 (c)2" 3y 6. Solve the following initial value problems:
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),...
(24 points) Find the general solution to each of the following differential equations dy a) = e)(x - 2). Over what interval is this solution valid? dx b) y" - 2y + y = (Hint use the method of variation of parameters) 1 + x2 c) y" - 8y' + 17y = 0. Is this solution (i) undamped, (ii) critically damped, (iii) under-damped, or (iv) over-damped?
4. (15 points) Find the general solution of the following second order differential equations. (a) y - 4y + 13y = 0 (b) y' +12y +36y = 0 (c) t’y" + 4ty' - 4y = 0