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Final Exam ??????? ?????? (1) ???? - 1 If $x_1(t)$ and $x_2(t)$ are solutions of $x'(t) + p(t)x = f(t)$; then $x(t) = x_1(t) + C(x_1(t) - x_2(t))$ with $C \in \mathbb{R}$ is the general solution of $x'(t) + p(t)x = f(t)$. Select one: O True O False

          Final Exam
??????? ?????? (1) ???? -
1
If $x_1(t)$ and $x_2(t)$ are solutions of $x'(t) + p(t)x = f(t)$;
then $x(t) = x_1(t) + C(x_1(t) - x_2(t))$ with $C \in \mathbb{R}$ is the
general solution of $x'(t) + p(t)x = f(t)$.
Select one:
O True
O False
        
Show more…
Final Exam
??????? ?????? (1) ???? -
1
If x1(t) and x2(t) are solutions of x'(t) + p(t)x = f(t);
then x(t) = x1(t) + C(x1(t) - x2(t)) with C ∈ℝ is the
general solution of x'(t) + p(t)x = f(t).
Select one:
O True
O False

Added by Nicole B.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Final Exam Mathematics (1) Theoretical - If x₁(t) and x₂(t) are solutions of x'(t) + p(t)x = f(t), then x(t) = x₁(t) + C(x₁(t) - x₂(t)) with C in R is the general solution of x'(t) + p(t)x = f(t). Select one: True False Final Exam If x₁ and x₂ are solutions of t + pt x = ft then t = t + Ct - 2t with C in R is the general solution of t + pt = ft. Select one: True False
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Transcript

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00:02 In first part, the given differential equation dy over dt is equal to 2y plus 10.
00:09 We need to check the solution, y of t is equal to 10 times of 8 2x2 of t negative 10 is the solution or not.
00:20 So now differentiate the y with respect to t.
00:26 So this is equal to 20, 8 to 2 twice of t.
00:31 Now this can be written as 20, 8 to the part twice of t, negative 20 plus 20.
00:40 This is equal to there are two as a common.
00:44 So we have 10.
00:46 8 to the power twice of t negative 10 plus 20.
00:51 And this value is equal to 2y plus 20.
00:58 It implies...
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