Find The Pollowrng in tograls:- Excersises 4 ( 2x + 6y x*) dy de (2 (ay + 29) dë dy + +) dy da x+4

Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: If f(x, y) = xe2y + 6xy, then is dydx given by: e2y + 6 등 2e2y + 6 2 O None of these O 2xe2y + 6…

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Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: Suppose that f(x, y) = e-2r² – 1y² + 2x +8y then find the discriminantD= faz fyy – fay- Question…

A: Solution: The objective is to find the discriminant

Q: dy Let y = (x2 – vx)4". Find using any method. dx -

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Q: Use the trapezoidal rule with n = 5to estimate V7 + y³dy

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Q: Solve the homogenous differential equation.

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Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: Ifx' +y +z -2aņz =1, then show that V1-x dy 1- y V1-:

A: We have to use the given condition x2+y2+z2-2xyz=1 to find this.

Q: find the Lineartransfromation T:Manz (R)R whose matrit Mp --

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Q: dy let y = xtan z then is da elect

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Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

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Q: d²y Given that x3 + y³ = 2, prove that 4х %3D dx2 y5

A: Given problem:-

Q: dy dt 1. y=V(3t2 - 2t + 1)(t2 – 1), 12/07/2021 18: 54

A: Given that       y = √(3t2-2t+1)(t2-1)  Here we have to find dy/dt .

Q: If f(x, y) = 8xey + 8y Inx, then is given by:

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Q: Consider the IVP y" + 2y' + 6y = 0, y(0) = 2, y'(0) = 3 > 0. %3D %3D

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Q: Use the method of undeterminad Coefficiento to slve the initial valene proalem : yo +Qy'+5y=cin…

A: The given initial value problem is              y''+2y'+5y=e-tsin(2t)  , y(0)=1, y'(0)=0 We find the…

Q: If f(x, y) = 8xe2y + 8y Inx, then is given by:

A: The given function is: f(x,y)=8xe2y+8y ln x Now, ∂f∂x=∂∂x8xe2y+8y ln x       =8e2y+8yx

Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? Select the correct response: y 2y O -2y O…

A: Topic:- non exact differential equations

Q: Express the solution of the follawing IVP in terms of the convolution integral: y" + 4y' + Hygt)…

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Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: Find Vq if (a) =In (r) %3D (b) p= In (-) %3D We know r= /x² + y² + z2

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Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

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Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

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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: if y=Asinx+Bcosx then prove d2y/dx2+y=0

A: Given,

Q: H.w use Gramer Rule to Fird XIZ -2X-y+2 -3 %3D -2x43y- 221

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Q: 4) Lett =,u = x? - y² ,v = 4xy³. Find %3D ax ду

A: t=uv

Q: Be. La ecuación diferencial (4x²y² + 6x y)dx + (5x³y + 8x²)dy = 0 tiene un factor integrante de la…

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Q: xy Let z . Then: 4x2 – 5y? | az dz ду

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Q: (b) / / | /3(x² + y²)dV, where V is bounded by y = 2r² + 2:² and y = 8.

A: The given question seems to be incorrect. The function inside the given square root should be…

Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: If f(x, y) = xe³y + 4xy, then is given by: dydx 3xe3y + 4 3e3y + 4 xe3y + 4 3 e3y + 4 3

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Q: 5) *=ClSln t ,y =4 csst t=-2 %3D a) determine dy b) and graeh

A: we have to find derivative

Q: Findd Fhie boundled by Ahe Cureo area 2. X= 3J-y' and x+Y=3 ーレ

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Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

Q: Wz bisects 2XZY and LX LY. Which choice of method can be used to prove 4XWZ AYW O SS O AAA O SAS AAS

A: We need to find congruence of ∆xwz and ∆ywz.

Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: dz for z = da z In(zy) + y, y = c os (x² + 1)

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Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

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Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy – 4y. Then:

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Q: Let z = exsec y Find d²z dxdy and d²z dydx

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Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Q: 4. Show that 4= 3y'z' i+4x²:* j+6x°y°k is solenoidal.

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