R= { (x, y) : y 2r+1}

Q: Vy - y 3 b) dy 2 y²

A:

Q: y' + z' - 2y = 1 z – y' = t %3D Yo = 20 = 1 %3D -

A:

Q: y (z² + yf) dz – a (z² – y²) dy = 0 %3D

A: Use substitution

Q: 4-у2 r2x+y dzdædy -V4-y2 Jo

A:

Q: b. min f (x, y) = 3x² – y² s.t. 2х — 4у 3D —11

A: Minimum value of function is determined using lagrange multiplier and its value is -33/4.

Q: y'' – y" + 4y'- 4y = 10e-t, y(0) = 5, y'(0) = -2, y"(0) = 0 %3D %3D

A: Given differential equation is y'''−y''+4y'−4y=10e−t, y0=5,y'0=−2 and y''0=0 Take Laplace transform…

Q: Use separation of variables to find an explicit solution. xyy' = 2xy² + y² %3D

A: Follow the steps below to solve a differential equation by the variable separation method. First,…

Q: ( b. F = y х )j+ + y 1+x?yz?+ + (1-y²z² 1+x2у2 V1-y2z²,

A:

Q: rx dydx Vx2+y2 0.

A: We solve this double integration problem by substitution method as given below in solution

Q: a) sec²t + dt 2 + V5 b) ys – 2y c) - dy

A:

Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

A:

Q: ux.ュメトXス1いスコ-Y Palx, utェッズ)-。 入2コメ; +メュ-」+5- メレ 2 d、しズuメッ]= xit Xzメ]-6 fnd in Ganeral rm.

A:

Q: f(x, y) = 2x – x² – y? %3D -

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

Q: %3D 0 аnd y' ) = vz 2. у(x) %3D Сisin2x + Czcos2x + 1; C1 = C2

A: Given  y(x) = C1sin2x+C2cos2x+1 On applying the initial condition yπ8 = 0 , we get yπ8 =…

Q: y'(t) = In(y- 3) %3D

A:

Q: 10et --2 Use lap lay trensform system dy, to find the solution of the 1 dx -24, + Y3 +Y2 XP

A: Given system is dy1dx-y2=04y1+dy2dx-4y2-2y3=0-2y1+y2+dy3dx+y3=0 From the first equation of the…

Q: X」+iyュ-Xz+iy2* =xロ Y」=V,ロ しr%3DV 2.

A:

Q: dy re: (e + e-")- = y² (separation of variables) da

A: Given that: (ex+e-x)dydx=y2

Q: Solve Xy"-xy' +y = a+3ln(x), y)=Q , yl)=1 %3D

A:

Q: find dy/dx

A: Known formula: ddx∫rxqxftdt=fqx q'x-frx r'x.

Q: dy = -1-yy2Yュ- GD %3D

A: Given

Q: y(t) = y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = -1

A: Given

Q: Dyy 2y-x; %3D

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Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

A:

Q: dz (D2 + 16) (D² + 4D – 5) (D² + 2D - 3)*z = 0, Dz = dr

A:

Q: Find dy2 of z = 2x – 5xy² + x² y° %3D -

A:

Q: Q3:A/ Find: dy dy y 2 Vy (1 + Vý)² yV4y? – 1 |

A:

Q: Non Homogeneous (D2 − 3D + 2)y = 5e2x

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Q: [v= -y +2x ,x' = 4y + x + t

A:

Q: dy Find dz given that y = -2 – 8z². z=-3

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Q: dy 3ry? + 10xy + (3x²y+ 5x² – 1) Y dx - Has solutions of form F(x, y) c where F(x, y) =

A:

Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: Coute : 2y da + 3x dy, where D is described by 0 < a < 1, 0 < y < 1.

A: We have to find the given integral. For this we can use Green's theorem

Q: d³y of y = (3x*-5)(2x³+9x-6) Determine the %3D dx3 7x5

A:

Q: 2. (D2 + 3D)y = -18x: v = 0. Dy = 5 when x = 0

A: Given differential equation is  D2+3Dy=-18x  and the given conditions are y=0, Dy=5 when x=0 find…

Q: D.Linear Homogeneous DE with Constant Coefficients: 2. (D2 – 2D – 3)y = 0 ; x = 0; y = 0; y' = -4

A:

Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. y =c,e+ce+c,e²r+c,cosx + c zsinx y =…

A:

Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as

Q: (D - 2D + 4)y = 0 ; y= - 2, Dy = 8, D²y = 0, when x = 0.

A:

Q: u³ = a²t , find d’u %3D dt3 2a4 а. 9u5 10a6 27u8 -10a6 С. Zu® 40a6 d. U8 b.

A: A detailed solution is given below

Q: y(2x- xy ty')da-x (2x-y) dy =0, when x(4):0 %3D

A: Given: y(2x² - xy + y²)dx - x²(2x - y)dy = 0, when x(1/2) = 0

Q: y = 1+(t- y), 2<153, y(2) = 1, with h = 0.5 %3D %3D

A:

Q: 4. (Dª + 2D³ – 6D² – 16D – 8)y = 0 - - - %3D

A: The given differential equation,     D4+2D3-6D2-16D-8y=0

Q: y² = 8x,x=2, AOR = Y AXIS

A:

Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: (y – Jx² + y² )dx -xdy = 0, when x = v3 and y = 1

A:

Q: d²y Find dy 34 y3 %3D こX+

A: Answer

Q: What is the y=x excos 2x? (A (B) (D²+5)² C D²+5 D (D²-2D+5)² D²-2D+5 annihilator for G

A: Solution

Q: 3.) y = Vr, y = 3, x = 0 around the x axis.

A: To find: The volume of the solid that is generated by the revolving the given function y=x around…