S: dx V4 + x² (a)by parts, letting dv = dx V4 + x² (b)by substitution, letting u = 4 + x2 3.

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: S when メ=2 Y =x*+b $ Find dy when X=. dt dy

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Q: dy Find the General and Particular solution of dx 3y; y=3, when x=0

A: The differential equation is given as dydx = 3ydyy = 3dx∫dyy = 3∫dxlny = 3x+lnAlny-lnA = 3xlnyA =…

Q: Determine dy for y=VX2+1 . dx2 alx

A: Obtain the second derivative as follows.

Q: 4 dx. x'V16-x (c) By using x= 4sin (0), find

A: We have to find integration by substitution

Q: t2 + 4t + 10 -dt t3 + 2t² + 5t dy J 3 + 5cosy

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Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: dy If y = In (x + Vx² + 1) then dx O A. x²+1 O B. 1 Vx? +1 OC. 1 O D. 1 x2 +1

A: Answer is mentioned below

Q: dy when t = 7. dx Evaluate y = 2z? – 3z + 5 x = 4t +t t = z? +z+1

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below

Q: Find the total differential. z = 10x5, y7 dz =

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Q: Integrate by Substitution. 1. dx where u = Vx+2 2Vx+2

A: By using substitution method, we calculate the given integral.

Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

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Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

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Q: Q4. If y= f (t) and x=f (t) d²y dx2 dy 3 and %D 4t dx2 dy By using chain rule, find dt

A: Chain rule is given by dy/dx=( dy/dt )× (dt/dx)

Q: dxdy Vy X'

A: Given: ∫01∫yy21y2-x2dxdy

Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2

Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

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Q: C/ Answer two only: dy dy 1- y= eV1+5x? the dx 3- y= 2r° +3 , x =, he .(using chain rule). dx dy 2-…

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Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

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Q: What is / - z dx? 1-x² o f- dx = -2cos-lx + C V1-x2 S- dx = 2sin-lx + C (1–x2 S-d 2 dx = 2cos-x + C…

A: 1. I=∫-21-x2dx =-2∫11-x2dx =-2sin-1x+C    ∵As ddx(sin-1x+C)=11-x2⇒∫11-x2dx=sin-1x+C=-cos-1x+C…

Q: d Evaluate In(et – t²)dt. Briefly explain your answer. dx '1

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Q: Q4: Given: d²y =[f(x-t)dt -show that = f (x)· dx? y %3D .2

A: Differentiation of integration

Q: dy when t = 7. dx 13. Evaluate y = 2z? – 3z + 5 x = 4t' +t t = z? + z+1

A: Derivative of the function decides whether the function is increasing or decreasing. If the first…

Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

Q: d csinx 1 dt 1-t2 dx '3 V5 SNt VE2 + 1 dt 1+xv

A: We have to solve the integral

Q: Find d²y csinx if dx2 Lm VE2 +5 dt + sinx = y – x secx

A: We can use the fundamental theorem of derivative  In order to solve the given problem.

Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: Integrate تلد ا - تم( فیگ S (a² – v²) * 22)* dv where " a" is constant

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Q: Find the total differential. z = 6x1°y8 dz =

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Q: dy اذا كانت y = 3z2 + (sin(z وكان = *3ez؟ 4 : أحسب dx

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Q: What is the I.F of dy/dx = y - xy^3e^(-2x)?

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Q: Let y(x) be the solution of the IVP dy - (y - 3)'dx = 0, y(0)=2. Evaluate y(13).

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Q: Find the total differential. z = 10x4y5 dz = (No Response)

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Q: d²y csinx Find if t Vt2 + 5 dt + sinx = y – x secx dx2

A: We will first find the first order derivatives using Newton-Leibnitiz theorem. The , we will find…

Q: Find dx/dt. Uince x² + y^ = 225, then. 2x dx dt 2y.dy 24- ニ

A: Given that x2+y2=225 we have to find the value of dxdt.

Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

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Q: What is the differential of x = 5y + 7y4 + 6y? – 8y3 ? O dy = (28y3 – 24y² + 12y + 5) da -- O dx…

A: Using differentiation ,

Q: b) Find if dx2 d²y Lm Vt2 + 5 dt + sinx = y – x secx rsinx

A: We will first find the first order derivatives using Newton-Leibnitiz theorem. The , we will find…

Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: Q2) Evaluate , S2 xsiny? dy dx 0 Jx2

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Q: dx - is 2/x - Sin| x +s|+c. Vx +5 The antiderivativeof - A) True B False

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Q: Q1/ Evaluate 1 dx Jo 1+x² using Simpson's 1/3 rule Simpson's 3/8 rule i- ii-

A: Simpson's rules are techniques of numerical integration. Both 1/3 and 3/8 rules are explained in the…

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

A: Find the integrating factor

Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: Find dx/dt when y=2 and dy/dt=3,given that x^3=9y^3-64

A: Find dx/dt when y=2 and dy/dt = 3, given that x^3 = 9y^3 – 64.

Q: ds Find where Vt +s = 2s . %3D dt

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Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…

Q: Find dy/dx by the implicet differentiasion x2+y2=64

A: