21. Determine the largest interval on which a unique solution of the following initial value problem is sure to exist? 1 tant *(f - 9)y" - ," + y(1) = 0, y'(1) = -1 2 -t° t+4' O (-2,0) ㅇ (0, 1) O (0,3) ㅇ (0, 플) ㅇ (-2,3)

Q: Determine the equation of the tangent line for y = sech(In x) + tan-(x²) tangent at x = e*. A. Yr =…

A: The equation of the  tangent line for the function f(x) at the point x=a is, y-fa=f'ax-a. The…

Q: 6. Find y' if y = ecotx? A. -2x [csc²(x²)] (ecotx") B. -[ csc (x*)] (ecotx") C. [cot(x²)]…

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Q: y=Arccos (x²)

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Q: If y = cos*[sec2 (30)], and (6 y will be equal to? 9.

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Q: 29 Given that at any point (x, y) on a curve, y = 2, and an equation of the tangent line to the…

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Q: the line 3x+ y=l is the tangent line for the graph of y= f(x) at x=1, then f'(1)= 1 (C) 1 (D) 3 A) 3…

A: The slope of the line y=mx+c is m. The slope is equal to the derivative of y i.e., f'y=m

Q: 9. y- 6r - 10r - 5

A:

Q: What is the slope of the tangent line to the graph of the solution of y' = 5√y + 3x³ that passes…

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: The integrating factor (IF) of the equation y' - 2ycot2x O A. sin2x O B. cot2x O C. Lnsin2x…

A: Solution:  To find the integrating factor of the given differential equations

Q: tS W C (b) Suppose that a function h is such that h(-1) 5 and h'(x) 2x +3. Find the equation of the…

A: The derivative of the function h(x) is given by,

Q: Q.1 In the study offrost penetration in highway engineering the temperature T at time t hours and…

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Q: y' = 3√y + 6x³ 3

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Q: Longest interval for (t+2)y’’-(sint)y’+ty/t-4=e^2t/t y(-1)=0

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Q: 3. Find the *_ 2° L_weak derivative her XE [0,2TC] XE

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Q: Find the equation of the tangent line to the graph of y =f(x) at the point where x=-3 if f(-3) = 2…

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Q: Evaluate the derivative of the function y = 2tan ",²+In (e +e).

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Q: What is the first derivative of y=tanh(0³+30)? A y'=3(0²+1)sech (0²+30) dy =3(0²+ 1)sech²(0²+ 30) B…

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Q: 24)) Since the tangent of the curve y = x ^ 5 + ax - 3 at the point x = 1 is y = x -b, then b =?

A: Given that y=x-b is the tangent of the curve y=x5+ax-3 at the point x=1.

Q: 23: The equation of the tangent line to the graph of y = f(x) at x=-3, f(-3)=2 & f'(-3)=5 is a)…

A: We have to solve given problems:

Q: 61. Find the points on the graph of y2 = x³ – 3x +1 (Figure 10) where the tangent line is…

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Q: A function H is differentiable at x = 2. An equation for the line tangent to the graph of H at x = 2…

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Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.