for differential equations 1. Identify each of the following differential equations as either Separable, Homogeneous, Linear...
Use the method for solving Bernoulli equations to solve the following differential equation. dy dx +3y = e Xy - 8 Ignoring lost solutions, if any, the general solution is y=0 (Type an expression using x as the variable.)
Identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y alone (3x+3x - 3y)dx + (xy? - x-2)dy = 0 Select all that apply. A. has an integrating factor p(x) or p(y) not equal to a constant OB. linear OC. separable D. exact E. none of the above
Use the method for solving homogeneous equations to solve the following differential equation. 9(x2 + y2) dx + 4xy dy = 0 Ignoring lost solutions, if any, an implicit solution in the form F(x,y)=C is = C, where is an arbitrary constant (Type an expression using x and y as the variables.)
Consider the following linear system of differential equations: dx/dt = 2x-3y dy/dt = -x +4y (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given x(0) = 3 and y(0) = 4 (d) Verify the calculations with MATLAB
4. Consider the homogeneous differential equation dy d y dy-y=0 dx3 + dx2 dx - y (a) Show that 01 (C) = e is a solution. (b) Show that 02 (2) = e-* is a solution. (c) Show that 03 (x) = xe-" is a solution. (d) Determine the general solution to this homogeneous differential equation. (e) Show that p (2) = xe" is a particular solution to the differential equation dy dy dy dx3 d.x2 - y = 4e*...
i. 1. Answer each of the following For each of the following differential equations, state the order of the equation and state whether it is linear or nonlinear. If the differential equation is linear, state whether it is homogeneous or nonhomogeneous dy + + xy = sin x dx 2 a. dx2 b. x6y(5) – x2y'" – (cos x )y – ex = 0 ii. Find the value(s) of m so that the function y = xº, x 0 is...
Solve the following differential equations. d) a) x2 ay + xy = 1, ( y = Inx + 2 y(1) = 2 dx | e) x dy - 4y = xe* - 4y - Xe ( y = x5e*- x'e*+Cx4)
Find general solutions of the differential equations to x. 14. xy ry-уз 15. y +3y 3xe3 16. y 2-2xy y2 18. 2x2y-rly,-: уз 20. xy' +3y 3x-3/2 11. x2ys xy + 3y2 25. 2y + (x +1)y'-3x +3
please help me solve #1,2,3 !!! greatly appreciated (2.2 Homogeneous linear equations with constant coefficients 1. Find a fifth-order homogeneous linear differential equation with constant coefficients whose general solution is y = (1 + Cze* + czxe* + e-*(C4cos2x + cssin2x). 2. Solve 2y'' – 3y" – 8y' – 3y = 0. 3. Solve y" + y' + y = 0.
Identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y alone. (4x+3x - 3y)dx + (xy3 – x-2)dy = 0 Select all that apply. A. exact B. has an integrating factor u(x) or (y) not equal to a constant C. linear D. separable E. none of the above