Q2// A :- Compute for the following at t=1 z = re²", x = t², y =t-1

Q: dt 34. tan t/4 – sin² t dy - Vy dy 35. 36. yV3 + (In y)? x² 1 38. dx 4х + 5 37. :dx /x² + 2x + 5…

A: 34) Solve the integration:

Q: Calculate the energy coefficient from the first order if the infinite potential box is as uneasy as…

A: Given: φn=2LsinnπxLφ2=2∂Lsin2πx2L To find: Solution

Q: Find the function "y" that makes the integral stationary V1+y²y2

A: Please check step 2 for solution

Q: Without finding a potential function, determine if G : , 2y^x is conservative.

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Q: Differentiate with respect to t. y = 7sin(x - t) -(7sin(x-t)) = dt

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Q: Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

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Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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Q: 1 use the formula L = dt to find the length of the curve dt dt 1 X = y = t° for 0st s1

A: according to the guideline, we are allowed to answer the only the first question  please repost…

Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: dz Suppose that z = x³ – 3y?, x = 4(t³ – 1), and y = Int. Find using the Chain Rule. dt %3D -

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Q: Assume that after months, butterflies’ populace in 1000 is calculated as: f(w) = 12w + cos(16w)…

A: Given f(w) = 12w + cos(16w) +n * 100

Q: Find the value of dr/dt at t = 0 if r = (u2 + 7)^(1/3) and u^2t + u = 1.

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Q: Express the general solution of dy/dx = 1+ 2xy in terms of the error function erf(4) = dt.

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: u = t+1.3 -sin(u+t +5.09) with u(1) = 0.29 Let . Approximate the maximum value of ult) to 5…

A: If any function has a maximum value at a point , then at that point derivative of the function is…

Q: Q3) Find dy/dt of the function y = cos (5sin (t/3))

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Q: . Determine the solution of y dt + (2yt + 1) dy = 0given that given that y (-1) = Q Call

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Q: integral f t^3 In t dt

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Q: ify+. 1 -dt = xy rsecx Q3.a) Find if y + S V sint+1

A: According to our answering guideline we can answer only first question if multiple questions are…

Q: dy Q1) Compute for y(x) = sec (2x) + 2x-1 and dt x(t) = 4cos(t2) at t-1 %3D

A: From the given problem:   yx=sec32x+2x-1xt=4cost2   Now applying the chain rule:   dydt=dydx.dxdt…

Q: Integral of (dt)/(t^2sqrt(t^2-16))

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Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

Q: Let y(t) satisfies dy dt 3ty-t-t 1+t2 for t2 0, and y(t = 0) = 1. Show that y(t) S 1+t for t2 0.

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Q: Q2// A :-Compute for the following at t=1 z= ze", z =t, y=t1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to th indicated value. y' =…

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Q: (b) If dy/dt = 2, find dx/dt when x = dx dt

A: By differentiating we solve the function

Q: dy 3 4-1+2у, dt (0) = 1

A: Given dydt=4-t+2y   ; y(0)=1  with h=0.1

Q: Q3) Compute for y(x) = cos'(4vT)+ 5x and x(t) = 4 at t=1

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Q: (2t + 4 dt = J t² +1 antidifferentiation c) Evaluate (Don't forget to include the constant of.

A: Find the integration of (2t+4)/(t2 +1)

Q: Compute the length of the path r(t)= (t, 4t3/2, 2t3/2) over the interval 0st<3. Hint: The…

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Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: dz Find dt(t=1,s=0) when z = 2x3 + 15y3, where x = t2 - s and y =t+ 2s2

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Q: Find the value of dr / dt at t = 0 if r = (θ2 + 7)1/3 and θ2t + θ = 1.

A: Consider the provided equation, r=θ2+713 and θ2t+θ=1 Find the value of drdt at t=0. Apply the chain…

Q: Q) Compute for y(x) sec (2x) + 2x -1 and x(t) = 4cos(t) at t-1

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Q: Let y(t) satisfies dy 3ty-t-t for t20, dt 1+t2 and y(t 0) 1. Show that y(t) S1+t² for t2 0.

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Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 2, and dz/dt = 2. (Enter your answers as a…

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Q: Q3) Compute for y(x) = csc3(4x) + 2x – 3 and x(t) = 4sin t² at t=1 dt %3D

A: Let y(x)=csc3(4x)+2x-3 and x(t)=4sint2 Differentiate y(x) with respect to x…

Q: Consider the function Alt) = -2t + 10. Calculate At)dt by using 5.1 a graph and areas 5.2 a definite…

A: From the given function: ft=-2t+10 As we know that: The standard equation of the line…

Q: Create a second order DE (no need for IC's) whose sdution conuergio to O ao t+ o, without…

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Q: 2s Prove that L(t sin t) (s²+1)²

A: We can use the concept of Laplace transform in order to solve the given problem.

Q: Osx 5. Use the Second Fundamental Theorem to find : S V4- t3 dt (7 pts)

A: follow next step

Q: E. Find the orthogonal trajectories to the curve y = ax²- acx (s held fixed. %3D where a

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Q: Find the linearization of x = -1 f(x) = 3+ S sec(t – 1)dt at

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Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/cscx))

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Q: Assume x and y are functions of t. Evaluate dt for 4xeY12-In 729+61n x, with the conditions -6, x-3,…

A: Given that 4xey=12-ln729+6 lnx and the conditions are dxdt=6 , x=3, y=0  find dydt

Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

A: 2. We need to determine the solution of the differential…

Q: Q2/ Express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

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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.