z 1 dz 54. z(z 4)

Q: z dz 2). S: 25+16z2

A: We can find the integration as below.

Q: 5. +xy+y =3 at (1.1)

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: D = (z + 1)(z – 1)(z² -

A: Given function is: w=z+1z-1z2+1 We have to find dwdz.

Q: Find the general cowtion of the die. y9) + ya) - 24 =-e (9+67x+17 x²) + (861nax - o cosex) „(2).…

A: The given differential equation is , y(3)+y(2)-2y = -e3x(9+67x+17x2) +…

Q: 4 x2 + 4

A: We have to find out the antiderivative

Q: 1 dz (z + 1)°(2:² + 4z – 34)i

A: Solve, as follows:

Q: dy Find if y 3e2 3z 一山 %3D O -9e 2

A: Using chain rule of differentiation.

Q: dy 2ty ii) 12+1 - 21 – (2 – In(t² +1)) = 0; y(5) = 0

A: Differential equation of the form Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x Given differential…

Q: 6. +4y> S 7. 15m+42s 8. pe-5 9. 52x+y 10. -zy-3r +S ame Cortesian anc

A:

Q: Evaluate the integrals

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

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

A:

Q: 5. (D³2D+4)y=0; y = -2, Dy = 8, D²y = 0, when x = 0.

A:

Q: L[(t + 1)2e] = ? %3D s2-1 s2 +1 (s-1)2 (s – 1)2 -

A:

Q: 2t + 3 r(t) -, In(t² + 2) t2 +1

A:

Q: Suppose that W (y1, Y2) (t) = 4, and y3 Yı – 3y2. What is W (y1, Y3) (t)?

A: Correct option -12 We have to find out the value for Wy1,y3t.

Q: 2y*+1 dy 3

A:

Q: Q1: 2ty 2t – (2 – In(t + 1)) y = 0 y (5) = 0 t2 +1

A:

Q: бу — 7 dy J (2y + 1) (4y² + 1) 11.

A:

Q: 3 Evaluate 2z (4 – a – y) dy dæ.

A:

Q: 8. fz/25 – z² dz

A: Consider the provided integral, ∫z225-z2dz Evaluate the provided integral. Apply the method of…

Q: 2こx+iy 2 Recz) =l 3-i1 if 121 =2, then

A:

Q: dy If y = e7z+16 then- dx O 112e7z+16 O 8e7z+16 O 6e7z+16 O 7e7z+16 O 16e7z+16

A:

Q: 4". Sy' 8y Sx'e* y10)=8, y'l0).S X-

A:

Q: 4 Evaluate: ₁₂ (4x²y – z³) dz dy dx

A: We can evaluate the integral  ∫13∫-24∫10(4x2y-z3)dzdydx.

Q: 3. y = x³ – 3(x² + w²) 4. y = x7 + V7x - 1 TT + 1

A: Differentiation wrt x

Q: 2dt J (t - 3)V2 – 6t + 5

A: Given that: ∫2dt(t-3)t2-6t+5

Q: (w°t wz? -z) dw +(z² tw² -w) dz= 0

A: Let's find.

Q: dy dt = y(у — 4)(у — 8), до 20

A: see my solution

Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

A:

Q: [2r] = [z] + %3D

A:

Q: Q2 by using Simpsons Rule method to find ,n=6 5 1 dx х 2

A: use sub interval for finding the integral.

Q: 2. dy 5y=Dy

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: Q.1) Evaluate, (a) 3y In (y) dy 7+1 zp- (ь)

A: Find the integral

Q: VZ (k=1)

A:

Q: 2.3 - y 5e2, with y(0) = 0 and y'(0) = 1 %3D

A:

Q: dy 3. 9-49y²

A: To find out the integration.

Q: r z+9z-2z2+19z-8 (z²+4)² dx

A: Given: ∫x5+9x3-2x2+19x-8(x2+4)2dx first, we perform a long division for the integrand. then use the…

Q: dz and dz if rys + y2³ + zr³ = 7. Find

A:

Q: t) = y"+y= √2sin(√√√2t), y(0)=9, y'(0) = 0

A: Given,        y''+y=2sin2t, y(0)=9, y'(0)=0

Q: 33) - 2y + y, + y; = 0, y + y', = 4t +2, y, (0) = y, (0) = y,(0) = 0 y + y, = t² +2

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: (zin z + 5)dz

A: The given integral is [xlnx+5] limit from 1 to 3.

Q: 87 V 174x-x2 9Vx2+y2 dydx = %3D

A: