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Solve the following differential equations using classical
Chapter 1, Problem 20(choose chapter or problem)
Solve the following differential equations using classical methods. Assume zero initial conditions. [Review]
a. \(\frac{d x}{d t}+7 x=5 \cos 2 t\)
b. \(\frac{d^2 x}{d t^2}+6 \frac{d x}{d t}+8 x=5 \sin 3 t\)
c. \(\frac{d^2 x}{d t^2}+8 \frac{d x}{d t}+25 x=10 u(t)\)
Questions & Answers
QUESTION:
Solve the following differential equations using classical methods. Assume zero initial conditions. [Review]
a. \(\frac{d x}{d t}+7 x=5 \cos 2 t\)
b. \(\frac{d^2 x}{d t^2}+6 \frac{d x}{d t}+8 x=5 \sin 3 t\)
c. \(\frac{d^2 x}{d t^2}+8 \frac{d x}{d t}+25 x=10 u(t)\)
ANSWER:Step 1 of 3
a)
The corresponding characteristic equation for the homogeneous solution of the form 
For the particular solution, we assume the solution to be of the form 
Substituting these in the differential equation to get the values of 
On comparing coefficients of like terms:
Solving the above two equations give :
Thus, the solution,
With the initial condition,
Final solution:
