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Find the general solution following second-order differential equations
4. (15 points) Find the general solution of the following second order differential equations. (a) y - 4y + 13y = 0 (b) y' +12y +36y = 0 (c) t’y" + 4ty' - 4y = 0
Find the general solution of the given second-order differential equation 3y" + y = 0 y(x) = _______
4. Find a particular solution and then the general solution of a nonhomogeneous second order differential equation y" - 2y' - 3y = 4e7-9
4. Find a particular solution and then the general solution of a nonhomogeneous second order differential equation y" – 2y' – 3y = 4e* – 9
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
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
(a) Find the general solution of the following second order linear differential equation given that y1 = t is known to be a solution: t2y" - (t2 + 2t) y' + (t + 2)y = 0, t> 0. (b) Find the particular solution given that y(1) = 7 and y'(1) = 4.
Find the general solution of the second order ordinary differential equation: y"4y 3sin2t
Find the general solution of the given second-order differential equation. y'' + 10y' + 25y = 0 Solve the given differential equation by undetermined coefficients. y'' + 4y = 2 sin 2x Solve the given differential equation by undetermined coefficients. y'' − y' = −10
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...