x³-2y2 dy f) dx Hint: You know two methods that will work! 4xy

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: (3y + 2x) dx –x² dy = 0, given that x = 1, when y = 2

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Q: The particular solution of y(x+y)dx + (x +2y- 1)dy=0; y(0) = 2 by NEDE is

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Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

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Q: 1 Q2: Evaluate fo y² (x² + y²) dx dy

A: Given :∫01∫01-y2y2x2+y2dxdy

Q: (х + у+4)dx+ (x + у—3)dy %3 0

A: The differential equation M(x,y)dx+N(x,y)dy=0 is said to be exact if there exists a function f(x,y)…

Q: Find the general solution to dy/dx= 6-x^2/2y^3

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Q: 1 В(т, п) ym-1(a – y)"-'dy. am+n-1

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Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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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 x³ - 2y² f) 3 Hint: You know two methods that will work! %3D dx 4ху

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Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: Obtain the particular solution when x = 1 and y = 1 3 y°) dx 3 - x(x + y) dy = 0

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Q: Ex 21Eulers method dy-y= - y Xーツ ーメー

A: We have to use the Euler's Method to solve                           dydx=y'=x-yx+y, y0=1,…

Q: 2 (Dx-2Dx0y +Oy)u= 3Xy %3D AMS. 4

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Q: 1) = sinx + ytanx dy dx 2) x = y + x sin? 3) Prove that (2xy – 9x2)dx + (2y + x² + 1)dy = 0 is…

A: 1   dydx=sinx+ytanx        the equation can be written as standard form        dydx-ytanx=sinx…

Q: I. FIND THE GENERAL SOLUTION OF THE FOI dy dy = xy + 3x - 3x dx 1. dx

A: As per our guidelines we are supposed to answer only one question

Q: 5 If y = dy then dx %3D x+1

A: Given that: y=xx+15

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: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

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Q: Evaluate the double integral: 2 √ ² √² (3x² +9y²) dx dy 0

A: To solve the given double integral.

Q: Solve the I.V.P: dy = 6y²x; y(1) = 6y?r; %3D dx Oy 1 372-8 1 Oy = 8-3z2 Oy 1 8+3z? Oy = 1 !! 8-3z

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Q: 10) *- dy + 8, y(1) = 1 10) dx A) y = Vx + 8x - 8 В) у%3D 1 + 8x - 8 27 C) y =x + 8x + 10 D) y = +…

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Q: -2dх 38. y-2dx dy er e2x + 1' УО) %3D 1

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Q: I. Solve for the General or Particula 1. dy dx = 3x+xy² y+x²y

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Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

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Q: solve the DE:   (2y^3-x^3)dx+3xy^2dy=0 ; y(1)=1 using 3 methods.

A: Let's find.

Q: Find the particular solution: (y4 – 2xy) dx + 3.x² dy = 0; when x = 2, y = 1 %3D

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Q: y² + 5 dy J y²Cy² + 25)

A: Given problem:-

Q: Solve the particular solution of (xª + y³)dx – 2x° dy= 0 when x = 2, y = 3. -

A: We can rewrite the given equation as,  (xy+y3)dx = 2x3dy xydx+y3dx = 2x3dy

Q: C. dy b. 4 sin 2x> , y = 2, when x = 2 %3D dx dy С. dx = x + 3+ e2x>, y = -1, when x =

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Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: 13. dy/dt = y²(1-y)², -∞ <yo <∞

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Q: Find the general solution by means of separation of variables if: dy = xy -x dx

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Q: y' + 4y = e^(4t) %3D

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

A: Take integration on both side and then put initial value

Q: d²y 10 9y = e3x + sin 3x dx2

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Q: dy e2x -3 Find if y = In %3D dx 1-4x

A: SOLUTION-

Q: What is the general solution of (D² – 2D + 5) y = 0 ? - y = Cie + C2e3 %3D y = Cie cos 2x + C2e sin…

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Q: Find an implicit general solution of ( x² + dx + 1+ 4x²y², - y*) dy = 0 %3D 1+4x²y?

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Q: 2-dy dy. y2 dx 12 ナ /2

A: We have to solve the given equation. The given equation is 2-dydX=y2X2+yX+1    ......(1)

Q: 4(3x+ y – 2)dx – (3x + y)dy = 0

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Q: The value of the integral 1 2 x²y° dy dx is: 2..3 1

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Q: Find formulas for dy and Ay if y = 8x – 4. | dy Ay =

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Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

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

A: we need to find d2ydx2 from equation x3-y3=c3

Q: -3 -2 ²₁ ² [z³(x + y)³] dz dy dx

A:

Q: The particular solution of y(x+ y)dx + (x+ 2y- 1)dy=0; y(0)= 2 by NEDE is

A: Let's find.