Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e = 60'.

Q: zy dy de t 5/2/2/0

A: To evaluate : ∫032/2∫0xxy dy dx+∫32/23∫09-x2xy dy dx The general formula of integration is…

Q: If z = xe" and x = t2, y = Vt then the value of dz at t = 1 is equal to . dt Select one: True False

A: Solve the following

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: 2. dy sin x - y where f(n) = 0. %3D dx

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Q: 3. y = C( Sec x+ tan x)

A: Note: we get orthogonal trajectories of families of curves by 1.differentiating  curve 2. Then…

Q: 2x + 7x +3. If Ax = 0.3 at x = 4, use linear Let y approximation to estimate Ay %3D %3D %3D Ay =

A: Given y=2x2+7x+3 if ∆x=0.3 at x=4 we have to approximate ∆y using linear approximation.

Q: , X= sin ztS d= In Find dw 2- Cost

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Q: solve using Separation of Variables. dy dt = ry-3

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Q: Find the cifferential dy of the given funddtion. (Use "cx" for dx.) y- dy

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Q: dy dz Find at z = 1 if y = 4z +4 and = 2. dt

A: Given: y=4x2+4

Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: Use the trapezoid rule withn=4 to estimate dx . Answer must be in fraction.

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Q: integrate ƒ over the given curve. ƒ(x, y) = x3>y, C: y = x2/2, 0 <=x<= 2.

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

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Q: (a) A beam is fixed at its left end x = 0 but is simply sup- ported at the other end x = L. Show…

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Q: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: What is fx , where f (x, y, z) = (sin yz)ez3−z−1√y ?

A: Given, f (x, y, z) = (sin yz)ez3−z−1y

Q: Find the orthogonal trajectories of r= a sin? 0 where a be the arbitrary constant.

A: We have, r=a sin2θ .....................................................(1) Differentiating w.r.t.…

Q: Use runge-kutta method find an approximate value of y corresponding to x = 0. 1, given that: dy * =…

A: We have function f(x,y)=x+x2y, y0=1, and h=0.1. We have to use the Runge-Kutta method to find an…

Q: Find dydx? for f(x, y) = eXy

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Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

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Q: find dy/dt. y = (esin (t/2))3

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Q: Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: . On what interval is the curve y = . dt +t+ 2 concave downward?

A: For y to be concave downward, it's second derivative y''  < 0 We will use the Leibniz rule to…

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: We have given thatthe radius r and height h of a right circular cone are related to the cone’s…

Q: On what interval is the curve y = 0, v- [ t2 dt t2 +t + 2 concave downward?

A: NOTE: Refresh your page if you can't see any equations. . to find the inflection point, first, we…

Q: Use the trapezium rule to find [2" dx taking ordinates with interval 0.25, in three decimal places.

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Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: .A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Using double derivative test to get max value of x

Q: Give the family of orthogonal trajectories of y? = Cx° + 5.

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Q: Find the orthogonal trajectories of r^n= a^n cos . given that r(1) = 13

A: Hey there since you haven't mentioned any angle of cos therefore i am assuming it to be cos (n…

Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: 6. y = C Sin x 7. y = cx?

A: To determine the equation of the orthogonal trajectories of the following families curves: y=Csinx…

Q: If r = (cost)i + (sin t)j + 2tk, find r × dr/dt.

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Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: he The product of linear integration is where c t $ (2xy – x²) dx + (x + y²)dy, x = y? 30 y = x? ,…

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Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

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

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Q: The integrating factor of the equation (2 + y + x) dx + xydy = 0 is

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Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

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Q: Find the rate of change f(x, y) = In(2a² + 5y2) at (v2, v2) in the direction making a (positive)…

A: First we have to find the divergence of the given function.

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate ſ,(x3 + 1)dx.

A: To find: ∫-11x3 + 1dx using trapezoidal rule with n=4

Q: On what interval is the curve t2 dt t2 +t+2 y = concave downward?

A: The given curve is: y=∫0xt2t2+t+2dt Using fundamental theorem of Calculus says: ddx∫axf(t)dt=f(x)…

Q: Find dy/dx if y = J' V1 + ² dt. Explain the main steps in your calculation.

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Q: Use the Trapezoidal Rule with n = 4 to estimate f, x² dx. Compare the estimate with the exact value.

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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.