Can't solve the following second order differential equation:
f''(x)+3f'(x)+2=4t
Show full complementary function and particular integral working out, thanks in advance.
Can't solve the following second order differential equation: f''(x)+3f'(x)+2=4t Show full complementary...
A nonhomogeneous second-order linear equation and a complementary function ye are given below. Use the method of variation of parameters to find a particular solution of the given differential equation. Before applying the method of variation of parameters, divide the equation by its leading coefficient x2 to rewrite it in the standard form, y" + P(x)y'+Q(x)y = f(x) x2y"xy'y Inx; y c1 cos (In x) + c2 sin (In x) The particular solution is yo (x)
Solve the given integral equation or integro-differential equation for y(t). yʻce) + f(t-v1yv) dv = 4t, y(0)=0 y(t)
Solve the given integral equation or integro-differential equation for y(t). t y't) + f(t– vy(v) dv=4t, y(0) = 0 0 y(t) =
Consider the following second-order differential equation:(a) Is the operator L self-adjoint? (show your work) (b) Find yH. (c) Does this BVP problem have a unique solution? Do you need to use modified Green’s function to solve this problem? (d) Use the Green’s function or the modified Green’s function to solve this problem.
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt which models a forced oscillation in a damping material. For example, imagine moving your hand back and forth underwater. Write this equation as a set of coupled first order equations by doing the following: ·Define a new function g = f'(t). This gives you one of the two coupled equations. . Use the given ODE, g, and its derivatives to write the second first order equation. Both...
Can't use math lab show workings Differential Equation The following ordinary differential equation is to be solved using nu- merical methods. d + Bar = Ate - where A, 0,8 > 0 and x = x at t = 0. dt It is to be solved from t = 0 to t = 50.0. It has analytical solution r(t) = A te-al + A le-ale"), where A A B-a and A2 А (8 - a)2 Questions Answer the questions given...
A linear equation. Differentiate the first-order equation 1 (2- a2) (3.123) a2 linear, second-order differential equation with respect to c to derive Solve for the general solution to this ODE and show that it contains three arbitrary constants a Use equation (3.123) to eliminate one constant and rederive the catenary of equation y(x) a cosh A linear equation. Differentiate the first-order equation 1 (2- a2) (3.123) a2 linear, second-order differential equation with respect to c to derive Solve for the...
3. (a) Solve the first order differential equation x + 4y = x' +2. (b) Hence find the particular solution if y(2)
fill in the blank. Calc 2 Part a and b Consider the following differential equation by" + 3y - 3y = 0 Exercise (a) satisfy the equation? For what values of r does the function y = e Step 1 in the To determine the values of r for which er satisfies the differential equation, we substitute f(x) = e equation, 67"(x) + 3f'(x) - 3f(x) = 0. Thus, we need to find f'(x) and "(x). f'(X) = Click here...
2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change the above differential equation so that the general solution to the homogeneous equation will become c cos x + C sinx. c) (7 pnts) Solve the second order linear differential equation y" - y = 3e2x by using Variation of Parameters. 5. a) (7 pnts) Determine the general solution to the system...