Verify that the given function is a solution of the differential equation that follows it.
$$u(t)=C_1e^{10t}+C_2te^{10t}, u''(t)-20u'(t)+100u(t)=0$$
Perform the operation.
$$u''(t) = \boxed{}$$
What is the best next step?
A. Solve for u(t) in the differential equation.
B. Integrate both sides of the differential equation.
C. Differentiate both sides of the differential equation.
D. Substitute u, u', and u" into the differential equation
What is the result after simplifying?
A. $$u(t) = 10C_1e^{10t}$$
B. $$100C_2te^{10t}=0$$
C. $$u''(t)-20u'(t) + 100 = 0$$
D. $$0=0$$
How has the solution been verified.