please help me solve #1,2,3 !!! greatly appreciated
please help me solve #1,2,3 !!! greatly appreciated (2.2 Homogeneous linear equations with constant coefficients 1....
5. Solve the linear, constant coefficient ODE y" – 3y' + 2y = 0; y(0) = 0, y'(0) = 1. 6. Solve the IVP with Cauchy-Euler ODE x2y" - 4xy' + 6y = 0; y(1) = 2, y'(1) = 0. 7. Given that y = Ge3x + cze-5x is a solution of the homogeneous equation, use the Method of Undetermined Coefficients to find the general solution of the non-homogeneous ODE " + 2y' - 15y = 3x 8. A 2...
2nd order linear homogeneous Find the general solution to the following homogeneous differential equations (you answers must have two arbitrary constants (you may use any letters, for example p and q or m and n instead of ki and k2 - notation doesn't matter here]). y" + 2y' – 3y = 0 (b) 6y" – y-y=0 (c) y" + 5y = 0 (d) y" - 9y' +9y 0 The two constants, e.g. ki and k2, determine (and are determined by)...
for differential equations 1. Identify each of the following differential equations as either Separable, Homogeneous, Linear Bernoulli, or Exact and solve the equation using the method of the type you have identified. Many can be classified in multiple ways, it is not necessary to list all possibilities. (3xy2 +2ycos x)+y'-y sin x-x =0 Туре: A. dx General Solution: B. (4xy+xy)2x+ xy2 dx Туре: General Solution: Туре: C. y'y'y+1 General Solution: (3x'y+e')-(2y-x-xe)dy Туре: D. dx General Solution: Туре: dy E. =y(xy-1)...
2. (e) (7 points) Find a homogeneous linear differential equation with constant coefficients whose general solution is y = 4 + ce?* + Gxe7x.
Question 1. Solve the following 30d order homogeneous linear ODE which has constant coefficients y" +3y" - 4y'-6y = 0.
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...
Given the Homogeneous Linear Differential Equations with Constant Coefficients, determine the general solution y(v) + 4y(iv) + 5y“” – 6y' – 4y = 0 y(x) = cte* + c2e-2x + c4e +04e-* + e-* (c4Cos x + C5 Sen x) Answer:
please thanks 2. 124 points Solve the following higher order homogeneous linear differential equatil y®+8y® +16y" =0 1970 h quota 2y" – 3y - 8' – 3y = 0.08. Oda vaba ona bandar bo 500032 TOMTOM (6) + 2y()) – 3 (4) _4y +4Y" =0 y" - 6y" +12y – 7y=0
2. (Undetermined Coefficients... In Reverse) Find a second order linear equation L(y) = f(0) with constant coefficients whose general solution is: y=C et + Cell + tet (a) The solution contains three parts, so it must come from a nonhomogeneous equation. Using the two terms with undefined constant coefficients, find the characteristic equation for the homogeneous equation (h) Using the characteristic equation find the homogeneous differential equation. This should be the L(y) we're looking for. (c) Since we have used...
Find a second order linear equation L(y) = f(t) with constant coefficients whose general solution is: @ y=Cje24 + C261 + te3t @ (a) The solution contains three parts, so it must come from a nonhomogeneous equation. Using the two terms with undefined constant coefficients, find the characteristic equation for the homogeneous equation. (b) Using the characteristic equation find the homogeneous differential equation. This should be the L(y) we're looking for. (c) Since we have used two terms from the...