1. (10pts) Find the solution to the initial value problem for the following differential equations 1/'...
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...
Exact Differential Equations. Let y(x) be the solution of the following initial value problem: (cos z ln(2y = 8) + 2) + (x+4)=0, x(1) -- What is the value of y(+/2)? (a) 37 + 1. (b) 1/7- 2. (c) /3+ V. (d) 4+1/. (e) None.
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
show all working 2. Find the solution to the following differential equation with initial value (20 points) y" + 2y + 5y = 4e * cos(2x) with y(0) = 0 and y(0) = 1
Problem 2. (10pts.) Find the general solution to the system of differential equations y' = 2 - 2 z' = 5y + 42
1 Pedro) Solve the following system of differential equations with initial value condition "+ 2x + y = 0 1 ++2y = 0 with (0) (0) - and (0) - (0) = -1
Problem 4. (1 point) Find the solution to the linear system of differential equations 5x -8y 4x - 7y satisfying the initial conditions x(0) = 6 and y(0) = 4. x(1)
please solve number 4 Problem No.1 Solve the following first order differential equations by finding: a- Homogenous solution a. The particular solution b- The total (complete) solution for the corresponding initial conditions. Note: Answer all questions clearly and completely. 1- y' + 10y = 20; y(0) = 0 2- 4y' - 2y = 8; y(0) = 10 3- 10y' = 200; y(0) = -5 4- 2y' + 8y = 6cos(wt); y(0) = 0. Let o = 12 rads/sec.
exact differential equations 2. Solve the initial value problem: (2.1 – y) + (2y – r)y' = 0) with y(1) = 3. 3. Find the numerical value of b that makes the following differential equation exact. Then solve the differential equation using that value of b. (xy? + br’y) + (x + y)x+y = 0
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