y - and v- 6. y" - 3y + 2y = 2x2 + e* + 2xe + 4e

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: 1. y" - y' - 2y = e by D- %3D operator method

A: We have to find CF and PI

Q: y 10 (x, y) (6,2) -10-9 2 3 4 5 6 7 8 9 10 -1 -1 -7 - -2 -3 -4 -5 -7 y%3D 6 -8- - -10 tho distance…

A:

Q: 1 5earctan(y) dy -1//3 1+ y2 3 1+ у2

A:

Q: 6. S -3dy 2y2+14y+70

A:

Q: ation. 4x y"-5y' +3y = 0 around xo = 2 x) = a, (1 -- 2* + 103 1536 Ob. 11 103 y(2) = a, (1+*- 2) .…

A: Given that, 4x2y''-5y'+3y=0 The x2 can be rewritten as, x2=(x-2+2)2 =(x-2)2+4(x-2)+4 So the equation…

Q: elimination of first degree variable: 3x+y-z=11 x+3y-z=13 x+y-3z=11

A:

Q: (2xy+ 3x2)e, +(x² – 2yz + 2y)e,- (e2 + y?)e, olan f(x, y, z)

A: Given that the function is

Q: X2 , 1 avuu. 3 VA 3. x = y3, 0 sy s1 about y-axis.

A: Given function is x=y^3

Q: method of variation of parameters y+3y+2y3sin e^^x

A: To solve the differential equation by the method of variation of parameters.

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

A:

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

A:

Q: X1+iy,=X2+iy2" ューx,○ X =X ,=y,O *ュ=ソ,○

A:

Q: The Power Chain Rule simplifies computing the derivative of a powerof an expression

A: To find the derivative of a power of an expression using the chain rule. ddxe3x+1 Solution: Chain…

Q: x = 2 - t, y = 1 + t, z = 3t; x - y + 2z = (x, y, z) =

A:

Q: Find the solution (varition of parameter)   X2y11-2xy1+2y=x3sin x

A: According to the given information, it is required to find the solution of the given differential…

Q: find dy/dx

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

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

A:

Q: (2xy + 3x²)e, + (x² – 2yz + 2y)e,- (e2 +y²)e, olan f(x,y,z)

A:

Q: how can i find the vectorial equation for d1:3x/2=y-1 and d2:?x+y-6=0

A: Given: vector equation for  L1:   3x/2=y-1 l2  :   x+y-6=0

Q: SOWE FOR THE ORTHO GON AL TRAJECTORIES y² = 4x² (1-ex)

A:

Q: V2x-x2 SS2*-*" (x² + y²) dydx

A: Changing cartesian to polar coordinates: x2+y2=r2x=rcos θy= rsin θ x ranges from 0 to 2y ranges from…

Q: (i) Find the covariance of Y1 and Y2, Cy, Y,

A:

Q: .2 f(x, y, z) = 4xy – 8xyz + 7yz² f,(x. y, z) = &xy– 8yz fy(x, y, z) = | 4x- - 8x2 f.(x, y, z) =…

A: To find the first partial derivatives of: f(x,y,z)=4x2y-8xyz+7yz2

Q: y = sec* ( Vsin(2t)) sec³ 3.

A: The objective is to find the derivative.

Q: 2x +y-z=3 x- y+z=0 y+2z =1. Then x=

A: Given system of linear equations; 2x+y-z= 3 x-y+z = 0    y+2z=1 We can use Cramer's rule to solve…

Q: 1- z Res z(z + 1). Iz=00 a) 0 b) 1 c) -1 d) 2 ||

A: Res( f, ∞) = - Res 1z2f1z, 0

Q: xsin 1x Vx+1 2tan-x Vx+1 2tan-1x QI) Find of y=: e2x+1

A: We will find dy/dx as following .

Q: 1. y = - V2x +1 2. y = (x – 1)3 + 2 3. y =-1 2x

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: y'+2y/x=x, y(1)=2, y(2) using h=0.1

A: given :y'+2yx=xy(1)=2, y(2) using h=0.1

Q: 3x3+y² x²+y² .2 (x, y) ± (0; 0), ,2 ) f (x, y) = 1, (x, y) = (0; 0).

A:

Q: 2. x =1+y², x = 0, y = 1, y = 2 about the x – axis.

A:

Q: 2x + y + z = 1 X- y+4z = In1 x + 2y - 2z = 3

A: We will solve this equation with the substitution method. So first of all we will find anyone…

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: From the given information the given curves from which the volume is to be generated are:

Q: 2 (4-х2 2 The integral LG. -(x² + y² ) dzdxdy is Vx² +y? -2 J-/4- 2 C[* dzdrdo .3 dzdrd0 2 •T/2 2 p³…

A:

Q: Ar)- (xr+1 - })* + (%, – )* + (xr-1 - )* + (y. – )² + (x, – ) + (y+1 - }) + (x, – })* + (y.-1- }) -4…

A: Given that, Lhϕr, s=1△x2ϕr+1,s+ϕr-1, s+ϕr, s+1+ϕr, s-1-4ϕr,…

Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

A:

Q: X- 2,6,3,1 . yr 3,74.2 س ۲ / / إنا علمت بأن فيم كل من المتغيرين و و هي كالاتي :- 1) E, - E *) 2)…

A: The data values given is as follows x y 2 3 6 7 3 4 1 2

Q: 2 sec 0 r drde = x² + y² dydx %3D 0. True False Reset Selection

A:

Q: V1. y=x' +1, the axes, x=3; 0X 1 y =-, , y-axis , y=1 & y =3 ; OY

A: Here we have to find the volume.

Q: y = x"-9 (x 20) X=0, y=D, about the Xaxis %3D

A: To find the volume of curve , towards the rotation about x - axis.

Q: (2xy + 3x²)e +(x² – 2yz + 2y)e,y- (e² + y²)e, olan f(x, y,z)

A: Given

Q: 1 y" – 2y' + 2y y(4) = 0, 3 (4) = 0. -

A: Given: The given differential equation is y''-2y'+2y=1x, y4=0,y'4=0

Q: roblem. y" – 2y' + 2y = e-; y(0) = 0, y'(0) = 4 %3D

A:

Q: onsider the DE vy" – y' + y = 0. ) Is this DE linear? ) If it is linear, is it omogeneous?

A:

Q: b) y = -x -1 -u) 4 = 3x +5 -ài) a) 2x +3 %3D y = 4x -) -ài, Bub ci) from il cis from ei) Sub = 4n -…

A:

Q: x=k y=1. kER 2=k x=1+k y=k ,kER z=1+k x=1 kFR

A: we have to find the parametric equation of the line that passes through origin and A(1,0,1).

Q: y" = 4(y-x), 0 sxs1, y(0) = 0, y(1) = 2, %3D

A: To check: given 2(a)  has unique solution.

Q: 4. x = 9-y2 ,-2 <y S2 about y-axis vis

A:

Q: y = (2x + 1)v2x+1

A:

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.