Evaulate: 2 1 pr+y (x)dzdydx 0.

Q: Find d2y/dx2 implicitly in terms of x and y.

A: we have;  xy-1=2x+y2 ................................(1) differential equation with respect to x

Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: 13 [* Vx2 +y dydx 00

A:

Q: Find d2y/dx2 implicitly in terms of x and y. xy − 1 = 2x + y2

A: xy − 1 = 2x + y2 We need to find  d2y/dx2 implicitly in terms of x and y

Q: (tVE2 + y² – y)dt + (y/E² + y² – t)dy = 0o %3D |

A: We will find out the required solution.

Q: Show that y = ex + 3xex  is a solution of y"-2y'+y=0

A: The given differential equation is,

Q: (x-y-2)dk t3x ty-1)dy=0

A:

Q: 1-x² 2. , S. et²+y? dydx = (е-1) 4

A: We have to show that:  ∫01∫01-x2 ex2+y2 dy dx=π4(e-1)

Q: 18. V1+x dx 1-X

A:

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: Solve equatian. the differentiql dy = 80-2y * Such that y=70 when x=0

A:

Q: Resuelva yDx - 2(x+y) Dy=0 O x² + 2y = cy² Ox+2=cy² O x + 2y = cy² Ox+2y=c

A: Given differential equation y D x-2(x+y) D y=0 The objective is to solve the differential equation.

Q: 2 c4 e-x-2y dydx 2х

A: It is double integration problem

Q: What is the I.F of (2y^2+3x)dx+xydy=0?

A:

Q: 2. x3 - y3 = c³, find y" %3D HOOAT d²x 3. x* = at?, find dt2 1983

A:

Q: dy 15 +4y-042

A: ∫115+4y-4y2dy

Q: Y = 4x²-5 Vsx dy=?

A: We want to find derivative of y, The given expression for y is,               y=4x5-55x

Q: V16-y? /32–x²–y² V 22 dz dx dy

A:

Q: Solve for d2y/dx2 for x = u2 - 3 and y = 4u3 - 2u

A: Given x=u2-3 and y=4u3-2u. To find d2ydx2. Solution: We have, x=u2-3 Differentiating the given…

Q: I Solve the fllowing FODF 2y(x+y+2) dx + (y²-x²_ 4x-1)dy = o when x=2,y= 3

A:

Q: How I show that if Y=ax^2 that (d/dx)=2ax(d/dY)?

A: The given expression is y=ax2.In order to prove the given expression, use the following definition.

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

A:

Q: S. S. (x + 2y)dydx = 10, Jo a

A:

Q: d²y B Show whether y = Ax² + · x2 is a solution for x2- dy + x dx + 3y = 0 or not. dx2

A: If y=Ax2+Bx2 is a solution for x2d2ydx2+xdydx+3y=0...(1) then it satisfies equation (1).

Q: Find the yp of the equation (D2 +4y=asinax + 4e ex %3D

A:

Q: 3 V9-y s S f(1,y)dxdy. y)dzdy. y-3

A:

Q: a2z If z = In(x² + y²), find a²z + dx2 ду?

A: Given, z=lnx2+y2

Q: EX. Evaluate the JJ(X*+2xy+y") dydx when step size of x = 0-2 and step Size of y=o.5?

A: Given: ∫01∫02x2+2xy+y2dydx with a step size of x=0.2 and y=0.5.

Q: Find dydx for…

A: the given equation of the curve is: y3+y2-5y-x2+4=0 we have to find the value of dydx

Q: 8. dy V1+ /1+x -1

A: We need to evaluate the following integral ∫-18dy1+1+x

Q: -2x (x² + y²)dydx J.

A: ∫02∫x22x(x2+y2) dydx

Q: dy of y3Dx dr Find csc2r,

A:

Q: Find the su x² + y? :

A: The surface is given as z=xy. Take the derivative of the surface, z=xyfx=y, fy=x. The surface area…

Q: Find dydt at x=3 if y=4x^2−4 and dxdt=3

A: Given  Differentiating with respect to x, we get

Q: If feF - dr = Sc(4x + 4y²) dx + (x²y) dy, what is.

A:

Q: Н. W.: -1/3 6dx 2. V9x2+ 1 c2/3 dy

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

Q: 3 c2x S *x² dy dx 4.

A: Integral

Q: dy 1- S V9+y2

A:

Q: Evaluate the following integrals

A: The given integrals are,

Q: Solve using variaiton of parameter (D³ – 3D +2)y = (1+e2x)-1/2

A:

Q: (Think homogeneous) Solve explicitly (y² - xy) dx + x²2dy = 0

A:

Q: 41 82x-x2 9V x²+y? dydx =

A:

Q: | 3yVT – 3y² dy

A:

Q: Find DF of fcx,y)=x²e° at the point (-2,0)-

A:

Q: Q2 Find2 of y = 4x/x+ vã at x=1? %3D

A:

Q: 523 + 222 – 5 y = dy then dz 3x + 2

A: Consider the provided equation, y=5x3+2x2-53x2+2 Find the derivative of the equation with respect to…

Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

A: