ų (H)= - 2y, (t) + 24;(4)= Y,(4) - 2y, (t) +2t t 9,lFS +2

Q: Find fx, fy, Tz (3x2 + y2 + 2z²) f(x,y,z) = e - fx=

A: f =e-3x2-y2-2z2  For fx ,we take y and z as constant and x as variable.  fx=∂f∂x For fy , we take x…

Q: (2rz - yz)dr + (2yz – zr)dy – (² – xy + y²)dz = 0.

A: Given that, 2xz-yzdx+2yz-zxdy-x2-xy+y2dz=0

Q: d²y dy – 4 + 4y = e2t.t dt2 dt

A: our objective is to solve the differential equation

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: 2. y"-y-6y = u(t – 1) – u(t – 4); y(0) = 1, y(0) = -1

A:

Q: тахz %3D 2x + у S.t х+у<60 2х + у 2 40 y < 30 х, у 2 0

A: Linear programing is a mathematical techniques to optimize solution of given constraints.

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

A:

Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: Y Is the midpolnt of XZ.If XZ 8x-4 and YZ = 3x +1, find x.

A: Given Y is the mid-point of line segment XZ XZ = 8x-4 YZ = 3x+1   to solve the given question use…

Q: dy * + 2(t + 1)y² = 0, _y(0) = - ip 1/8

A:

Q: 1. (D³ + 3D² - 4D - 12)y = 0 2. - d'x 19+ 30 = 0 dt3 dt 3. (4D4 - 8D³ - 7D² + 11D + 6)y = 0

A: 1). From the given differential equation; D3+3D2-4D-12y=0 So, The auxiliary equation is:…

Q: Solve the IVP y" + 2y' + y = U (t – 3), y(0) = 0, y'(0) = 1. -

A:

Q: D={(x,y):4 < x² +y² < 81,< x <-V3y}, V3 Find [S, dA JJp y2

A: We will use polar co ordinates to solve the problem

Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: d²y dy +2 + 5y = 5t2 dt? dt

A:

Q: y"(t) – 4y'(t) + 4y(t) = 4e2t; y(0) = 1, y'(0) = -4

A: Given differential equation y''t−4y't+4yt=4e2t and y0=1, y'0=−4. Take Laplace transform both sides…

Q: z² - xy = 2 at the point (2, 1)= %3D

A: We have to find the slope of the line tangent  to the given curve.

Q: f(z, 9) = 82" + 5y² + 4z°y+ e7=y of Calculate

A:

Q: 2 c4 e-x-2y dydx 2х

A: It is double integration problem

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

A: Given

Q: Se-2t if 0 3,

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: W = / x2 + y² + z² Find Wx, Wy, Wxz,Wyy, Wzyx %3D

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: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: t2 d?y dt2 4t + 6y = t3 + 1 + 6y = t³ + 1 dt

A: Differential equation

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

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: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

A:

Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

A:

Q: 4. (D3 – 4D² + 4D)y = 0 5. (2D4 – 3D3 – 2D²)y = 0 - -

A: (4). The given differential equation is: D3-4D2+4Dy=0 So, the auxiliary equation is: m3-4m2+4m=0

Q: A particle moves on a vertical line so that its coordinate at time t is y=t3 - 12t + 3 , t>0. When…

A: (b)        y = t3 -12t+3    y1 =3t2 - 12 = v(t) when particle moving up means v(t)&gt;0    3t2…

Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

Q: Q5: 6y²dx-x(2x² + y)dy == 0 (Linear BernoullLeq.)

A:

Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as

Q: Q3: 1f f (x,y) = 6x*y5 + 4x*y4 Prove that: f (x,y) * fxxyy fxx * fyy = 1

A:

Q: Find Vy where = (x² + y² + z²) e¯¯ √√√x² + y² + z ²

A: Given :ψ=x2+y2+z2e-x2+y2+z2

Q: What is diffential equation of y"-5y'+4 when y(0)=1 and y'(0)=1

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: yz 4. II »z dr dy dz Jo

A:

Q: Solve for the DE of: y = C₁+C₂e7x O y'-+7y=0 Oy" - 7y¹ = 0 Oy'-7y=0 Oy" + 7y¹ = 0

A: The given equation is;  y=C1+C2e7x.

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

A:

Q: Solve the I.V.P: dy 1 = 6y'x; y(1) dæ 14 1 y = 3z2-17 y = 17-3z 1 Oy = 17-3z2 1 y = 17+32

A:

Q: Find S- y dy Vy+2 using the substitution u +5=√√y+2.

A:

Q: 18.t2y′′−4ty′+6y=0,t&gt;0;y1(t)=t2

A:

Q: dx Vx²-4x-7 7. dy y2-8y+5

A: