obtain just a particular solution (the general solution can always be obtained easily by adding an arbitrary multiple of a solution of the associated homogeneous equation). In these exercises, the forcing function is an elementary sinusoidal function. If the forcing function is cos 5t, then a particular solution of the form A cos 5t will not work. However, a linear combination of cos 5t and sin 5t will work. Thus, the form for xp is A cos 5t + B sin 5t, where the constants A and B are determined by substituting the assumed form of the particular solution into the differential equation for x. In Exercises 47–52, the forcing function has several different terms. Use a form for xp consisting of the sum of the forms for each term.
Transcribed Image Text:dx
51.
+x= 2e3 +sin t.
dt
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Expert Solution
Step 1
Given differential equation is Non-homogenous differential equation. Solution of this give differential equation is given by sum of Complementary function and particular integral that is (CF+PI).
CF is calculated by solving left hand side of the differential equation.
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