(1) Find a general solution to the following non homogeneous differential equation: y'' + 5y' + 6y = 6x^2 + 10x + 2 + 12 e^x; yp(x) = e^x + x^2 (2) Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equations (a) y'' - y' + y = (e^t + t)^2 (b) y'' + y' + y = e^t + 7 (c) y'' - 2y' + 3y = cosh t (3) Find general solution to the following differential equations: y'' + 4y = sin q - cos q y'' + y' - 12 y = e^t + e2t - 1 y'' - 4y' + 4y = t^2 e^t - e^(2t) (4) Find a particular solution to the given higher order differential equation: y^(4) - 5y'' + 4y = 10 cos t - 20 sin t

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section 4.5 #6,10,12,14,20,28,36,38
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(6) Find a general solution to the following non homogeneous differential equation:

y'' + 5y' + 6y = 6x^2 + 10x + 2 + 12 e^x; yp(x) = e^x + x^2

Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equations

(a) y'' - y' + y = (e^t + t)^2
(b) y'' + y' + y = e^t + 7
(c) y'' - 2y' + 3y = cosh t

Find general solution to the following differential equations:

(20) y'' + 4y = sin q - cos q
(28) y'' + y' - 12 y = e^t + e2t - 1
(36) y'' - 4y' + 4y = t^2 e^t - e^(2t)

Find a particular solution to the given higher order differential equation:

(38) y^(4) - 5y'' + 4y = 10 cos t - 20 sin t

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I have solved eight problems on differential equations. I have found general solutions and particular solutions to non homogeneous second order and higher order differential equations. I also have shown how to determine if the method of undetermined coefficients together with superposition can be utilized to solve given differential equations. This problem set contains a wide variety of problems encountered in upper level calculus course. This problem-solution set will be very useful in learning the solution process to differential equations and to prepare for upcoming examinations. Please download them for success in your calculus course.