Question Find the antiderivative of r' (t) = (est, e-7t₁ -&) that satisfies the initial condition r(-1) = (eº, - - 7,1). 6 e6 Sorry, that's incorrect. Try again? r(t) = )i + (1)j + (0) k

Q: Let us solve the following equation via separation of variables J²u(x, t) Ət² = 7 d²u(x, t) ?х2 a)…

A: The given equation is ∂2u(x,t)∂t2=7∂2u(x,t)∂x2. Solve the equation by using separation of variables.…

Q: Let 7 (t) = Find '(t) 7' (t) = ( -5 - 7t -77+-+2) 6t+1' -4t2 +4' -7t3 + 2

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: DIFFERENTIATE ITOU h(t)= 6t + 1 6t-1

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Q: ind y as a function of T if y" - 7y" +10y/ = 12e", %3D y' (0) = 11, y"(0) = 10.

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Q: If G(2) = S. 4t° -2t J-4x TeA _t² +3 dt, then G(x ) = 0. ett True False

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Q: 7x2. 7xy ly' = 48y – by² – 8xy 49x | - The critical point not on the axes is a(n) Select an answer…

A: Solution

Q: - lx + 2 -dx (x – 5)(x – 4) Evaluate + C

A: Here we can solve the integration as below

Q: Solve the equation Ut u(0, t) u(4, t) u(x, 0) - = 2urr 3 -5 = 2

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Q: Evaluate the following integral, where R is bounded by x = 1, y = 2x + 4, and y=-x-2. SS₂² dA R

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Q: For the slope field shown, which could be a family of anti-derivatives? y -6.28 6.28 O y = – cos x +…

A: Given slop field is Now we check all options one by one.   option 1: Given y=-cos(x)+C…

Q: form Demonstrate that the solution of dy = -1 yn+1 for any n = 1, 2, 3, 4, ... is always of the dt 1…

A: Step 1:Solution-True for any n=1,2,3,4---Step 2: Step 3: Step 4:

Q: For the slope field shown, which could be a family of anti-derivatives? TUN | 31 1112+\ll || \ ++~…

A: A slope field shows the slope of a differential equation at certain vertical and horizontal…