calenlate calculate SS(6-2)ds, SP(E- scone 2= VX2+y2 the port of between the T3E 2 and 2=4 plones.

Q: dy 4xy+5y2 The DE: can be transformed into a seperable DE %3D dx xy +3x2 in x and z by using the…

A: We have given a differential equation and we have to find substitution to make it variable…

Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

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Q: dw Use an appropriate form of the chain rule to find dt = In(10x² – 2y + l2³); x = tỉ, y = tỉ, z =t?…

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Q: 1- 2xy 7. y = %3D %3D ds e'-2t co dt 9,

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Q: d²x_dx Verify that x = C,e¬t + C2e2t is a solution to dt2 2х — 0. - dt

A: To verify the given statement.

Q: + (4xy – 3x²) dy = 0, find an integrating factor of the form d equation. %3D

A: First we have to find integrating factor for given differential equation and with the help of…

Q: dz 2. Given z = 4x2 + y²,x = sin t, y = t², find- %3D dt

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Q: 0. dy for y = 4t dt. 4t +1 3x3 Use Leibniz's rule to find хр

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Q: olve the equation x y² dy = (5 x³ + y³) dx using Homogeneous method.

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Q: d²y 1 dy y + y(3) = 0.009u, y(10) = 0.003s - dt2 t dt Use an appropriate method to find y(t).

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Q: 4. Find dy and Ay for y = 3/ – I+ 2x at r = 2 with da = Ar = 0.2.

A: Consider the following information: y=3x-1dx=∆x=0.2 Differentiate y with respect to x: dy=32x-1dx dy…

Q: Gixen dw wt 3y x dt dy +2X +3 x Find the gencral oludtii, usri eign.

A: Write the given system into matrix equation as follows.

Q: dz Use an appropriate form of the chain rule to find dt z = 8x"y³; x = t°, y = t Enter the answer in…

A: Topic :- Differentiation

Q: 2. Used Euler's method to approximate y (0.5) and y (1) for the I.V.P y' = y + xe2x, y(0) = 1.

A: Given y'=y+xe2xand y0=1

Q: Find the differential dy. (а) у — ху5 xv5 – x dy = (b) y = (1+x)-9 dy

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Q: Hiws slove du 4 dt %3D dx2 u(6,t) = L (8,t)=0 U(x, a) =0 : =4X-()x²

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Q: Find the general solution for dø = z(z – z²)sec²Ø %3D | dz

A: the given differential equation is: dϕdz=zz-z2sec2ϕ we have to find the general solution of the…

Q: dy -y2+1,ysCJse Cantial cokditian.

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Q: The solution of ë+w?x = fsin wt with initial conditions r(0) = 0 y a(0) = 0 is given by %3D %3D

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Q: SxY (@) = 0 and Sx (@) =0 if X(t) and Y(t) are orthogonal.

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Q: 15. What would you choose for your u here if you used integration by parts? f 3t e2" dt а. t b. e21…

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Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: Find the differential dy. (a) y = xV10 - x dy = -2 (b) y = (1+x) ? dy =

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Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1) = 8

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Q: Q. yrsy fase Jestell 4 cos 3t 24-24-fct) with Zero intiral locations гу чувст ostal 1<t<2 2 <t<3

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Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: Q4: Find the general solution of d?y dy - 3 - 4y 3e2t + 2sin t - 8et cos 2t, dt dy y(0) = 2, (0) %3…

A: Given that  The differential equation  To find the general solution

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: (x² + 2xy – 4y²)dx – (x² – 8xy – 4y²)dy = 0 - %3D -

A: Consider (x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0⇒ (x2+2xy-4y2)dx=(x2-8xy-4y2)dy⇒dydx=x2+2xy-4y2x2-8xy-4y2To…

Q: Q.2 Evaluate () dx. 2x (i) Using Trapezoidal rule by takingh = 0.2, h = 0.5 & h = 0.25. %3D %3D %3D…

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Q: Evaluate: J-1)–1) dy 0-my-1-등u-1)" + 즐피 ++ 11-arctan(Y )+c arctan () +c V3(2y+1) O-m-- 1³ + }n² +…

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Q: c3 Q3/ Evaluate , S(6x³ + 6y²) dx dy using Simpson's 1/3 rule in x-axis and Trapizodal rule in y…

A: Given ∫23∫466x3+6y2dxdy

Q: i x Jl plaly da :J,I Ji ull rcos(@), y=rsin(@) التكامل e-(5x2+2y) dxdy

A: We have to use integration using changing the rectangular axis.

Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21

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Q: Find the value of y(0.2) using fourth order Runge-Kutta's method from: dy -2.xy', y(0)=1. dx

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Q: ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds…

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Q: Find the general solution of this DE using INSPECTION. dnda + +(x? t y?)dx = 0 2 aycdly

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Q: Find the solution of ty -1 dt t'y 1 dy = 0 ty? O In t + 1 C ty %3D O -t-2 + 1 = C ty %3D Ct

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Q: dy 3. da + y = 2xy?e"

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Q: tione in detai 0 Ose dapaie teamfaven to rolve d'y + d dy ty=tet d+2 %3D dt with ylo)= 1 = %3D

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

A: From the above question, we get the differential equation dydx=-a2-x2x with the initial condition…

Q: Given z = 3x'y + V5 cos 2y-2x, detemine the total differential o

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Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: V4-x² E Evaluate the double integral (x² + y² )°dydx.

A: Convert Cartesian coordinate system into polar coordinates system.

Q: dy f(x.y), y(x,)=y, by Euler's method is dx The third approximate solution of

A: Let us consider differential equation: dydx=f(x,y),   yx0=y0 Approximate solution of differential…

Q: 5.Express this model of an electric circuit d² y dy +6¹ +5y=sin10t, y(0)= 0, y'(0) = 1 dt² dt As a…

A: First I have introduced two functions and then find pair of first order differential to the given…

Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

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…