Solve the following first-order ODE a. b. Solve the following second-order ODIE 2 =-200, 댓(z =...
Question 5 The ODE Y' +17xy= 2 xy2 is a exact ODE a. b. second order linear non homogeneous ODE Bernoulli equation c. d. linear non-homogeneous ODE
First-Order ODE (a) .Find the general solution of the following ODE: (b). Find the general solution (for x > 0) of the ODE : Hint: try the change of variables u ≜ x, v ≜ y/x. (c). Find the solution to the ODE that satisfies y(2) = 15. Hint: Try separation of variables. For integration, try partial fraction decomposition. 2Ꮖy 2 Ꭸ , . + <+5 12 , fi - z - ,fix = zu y' = y2...
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system of ODE using Laplace transform method: Xy-=5x1-2x2 + Mu(t-1) x2-=-2x1 + 2x2 x,(t) and x2(t) refer to the motions of the two masses. Consider these initial conditions: x1 (0) = 1, x; (0)-0, x2(0) = 3, x(0) 0 Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system...
5. Solve the initial-value problem associated with the linear first-order ODE z y + * In(x) y = 2e3x y(1) = 0, O O where the prime stands for differentiation with respect to x. O A. y = r-> (3x + Ke"), where K is an arbitrary constant. B.y=r" (e3+ Ke*), where K is an arbitrary constant. C.y=r-(+2 – 23). OD. y = x* (032 – *+2). O E. y = x-P(.38 – 42+2). OE y = x? (032 –...
Problem 3. A connection to second-onter ODE Recall the second-order ODE ay" + by' cy g(t), where a 0, b, and c are all constant and g(t) is the non-homogenous term. (a) Use a substitution to show that this ODE can be written as a vector equation их for a constant, 2 × 2 matrix A and vector functions x(t) and G(t) (b) Compute the characteristic equation of the matrix A, and relate this to the original second-order ODE. Problem...
Solve the following 1st order ODE: * + 5x = cos(2t) x(0) = 2
ODE - 1 Q.1 Solve the following first order linear initial value problems. (a) 2ndp - 0.4pdt -0, p(1)- 0.2 (b) v(f) dv (1) +*dt - 0, v(2) -2 + 2v ()- 6, v(0) - 10 (c) (d) The first order differential equation, initial value problem, - Sms, v(0) = 2ms. describes the motion of a car. Find an expression for the speed v () and determine the velocity of the car after 10 seconds from the beginning of its...
MATLAB HELP .. SHOW CODE PLEASE 3. Stiff ODE The following second-order ODE is considered to be stiff. entre = -1001 - 1000.54 With ’ode45' command and the initial condition y(0) = 2 and y'(0) = 0, - Save the y(t) 0 <t<15) on HW8_4.dat file - Save the 0(t) (0 <t <15) on HW8_5.dat file
Solve the following first order ODE with a given initial condition using Euler method in Excel using the formula given with n= 3, 10, and 100: y(n1)y(n)f(x(n), y(n)). dx (b-a) dx y'(x(n), y (n)) y'6where y (3) = 1 on the interval [3,6] b.y'yinwhere y (2)= e on the interval [2,5] a. Create a table for each n-values given and a graph one separately. Solve the following first order ODE with a given initial condition using Euler method in Excel...
The van der Pol equation is a second order ODE which is written as follows: 91 where μ > 0 is a scalar parameter. Rewrite this equation as a system of first-order ODEs and solve it using the Euler method for t E 10.2, where μ-1. Explain the physics behind vour numerical results. The van der Pol equation is a second order ODE which is written as follows: 91 where μ > 0 is a scalar parameter. Rewrite this equation...