For atims (3) to (8) refer to the À = x2i + (2x"-y)j - yzk and = 3x²y + y² z? followning = X? %3D (3) ♡ Ø (4) D.A

Q: The differential of y = (5x-6)e2z has the form | dy = (mx + b)e2# dz %3D Find the values of m and b.…

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Q: 4x Compute (2x + 4yz) dz dæ dy 1

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Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

A: Given:T"=6x2y3-cosx+5y2-siny+10x2-e-3xTo determine:i  T'=∫T"dxii  T'=∫T"dy

Q: d. Use your answers for parts a and b to estimate 1 -dx using the trapezoid rule with n=4

A: Approximate by trapezoid rule

Q: 1 In (a² + y? + 1) dædy -VI-y? |

A: I use polar conversion method to solve this double integral

Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

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Q: G YA PAZ E X F 7. PZ = 5 and GY 12. Find GP. (purple) %3D

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Q: Given dy dy dz² +2 + 5y = e dr and y(0) = 0 and = 0 find the value of y(0.1) and y'(0.1) using the…

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Q: 4. Evaluate: S. yx²dx + xzydy + xz?dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

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Q: Given y = x'e 2 2z - is: dy is: dz Solost ...

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Q: The approximation of I = (x-3)e* dx by composite Trapezoidal rule with %3D n=4 is:

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Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

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Q: Given the equation 2= 3x2 +1 with y(1) = 2. Estimate y(2) by Euler's method dx using h = 0.25. %3D

A: Note: Hi there! Thank you for posting the question. As there are several independent questions,…

Q: +00 1 1 : dx x[In(mx)]3 m+3 8

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Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

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Q: Given a+ yx = e¥ , what is 1-y dy dz 1+y dy 1+y dz 1+y el-I

A: Given equation is x+yx=ey We have to differentiate the given equation. To differentiate given…

Q: (b) Given that y(6x +1) e** = 1+ - In dy Find when x 0 and y=1. dx

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Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

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Q: Given the non exact DE y(8x-9y)dx+2x(x- 3v)dv=0. find f(x).

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Q: S S§y²cos(xy)dydx

A: we have given,                 ∫x =0x=1∫y=0y=π4y2cos(xy)dydx After arrangement,…

Q: Use the correet fransformation to Find the solution of the Problem below. 一00<Xく00 0< Y<1…

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Q: If y = f(x) is the solution of (5aty – 12a – 2y³)dx + (x³ + 4y³ – 6xy?)dy = 0, f(0) = 0, then

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Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: For the given DE with coefficients linear in two variables, do the following: (6x – 3y + 2)dx – (2x…

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Q: Find the Complete or Particular solution OF the Followoilng diffi rential equations: (2メコ+ )dx -2メよ…

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Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

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Q: 13. Differentiate y = e** with respect to x . ,3x+1 C (3x+1)e³x! D 3xe*+1 O A В D A

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Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: 6 If the substitution y = xº is made, the 64 3√√y 3 + √√y integral [ 1 dy will become

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Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: dy 2) Find implicitly: dx (a) xy+3x2 =y? (b) exy – Iny =x? %3D

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Q: Find the par ticular solution of the differencial 4. given x=0 and y= eguation dy -20cH1) (x+1)

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Q: (b) Solve the following initial vahue problem by separation of variable = 2x at x = 0, y=-2 dx

A: We will solve the problem

Q: If a = 5+ti and y = 3t - t then dy at t = 1 dz is :

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

Q: 1) Find the solution of the following equation: y"+ ly 0, with y (0) = 3 and'y (0) = 3 with A<0. Is…

A: Let λ=-a2&lt;0 Then, y"+λy=0 ⇒y"-a2y=0 Auxiliary equation is m2-a2=0 ⇒m=±a So, the general solution…

Q: [" In(y+z) e dxdzdy = [Show your solution.]

A: Given that,

Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

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Q: Given the IVP dy + 4y = x - 2, y(1) = 0, dx the value of y(2) is closest to

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Q: Find an upper bound for the error in estimating (5x3 + 2x)dx using the Trapezoidal Rule with n = 10…

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Q: If x = 5t +4 and y = 3t-7 , then find dy at t = 2. dx а. 1 O b. 2

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Q: Solve for the DE equation associated by the given function: у %3D Ае2* + Ве* + С. а.

A: the given solution of differential equation isy=Ae2x+Bex+C

Q: dy 13. y(1) = e de ar(In y - Inr + 1)'

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Q: Why is e^x selected as u and not e^2x (to get du /2 = e^x dx in the problem attached?

A: Consider the integral  ∫e2xe2x+3ex+2dx

Q: Given Z = ye 3r + 2y; where a = ln 2 and y = 2 with possible errors Ax = 0.01 and Ay = 0.03.…

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Q: 1- y? 1+ y 4 06: If x? dx Show that 1 %3D ,2 dy レアス+1.

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Q: If we have to check the DE (5-8y+4xy)dx = (x+2)²dy for Exact then My

A: M dx + N dy =0

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.