1. (D* + D' – 7D® + D° + 22D* – 22D³ – 20D² + 40D – 16) y = 0

Q: Obtain the solution using Integrating Factors Found by Inspection y(x3y3 + 2x2 − y)dx + x3 (xy3 −…

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Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

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Q: 2. y(3x* + x°y$)dx – 2x°dy = 0 (use integrable combination only) -

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Q: 2-) Calcu late +he folloming integ rols by using the integration met hods a)| (hx" +8x²+ 15x) dx dx…

A: We are allow to solve one que at a time

Q: Compute the differential dy for y = -6x° + 8x5. dy =

A: topic - differential equations

Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

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Q: Obtain the particular solution satisfying the initial condition indicated. (variable separable) dx…

A: Use the variable separable method and satisfy the initial condition. Also use the properties of…

Q: Express a general solution to 2x(1 – x)y" + (3 – 10x)y' – 6y = 0 Using Gaussian hypergeometric…

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Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: 1. 3(3x2 + y²)dx – 2xydy = 0

A: According to our guidelines we can solve only the first question. Please re post the other questions…

Q: 5. sinx+ cosh2y = 0. dy 6. /2xy -= 0. dy y

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Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: 」enr一2) dz csc (4r – z) dz dz dz 17. 2 V1 – sen 2z V1 – cos (4- – 2z) In | csc (4- – z) – cot (†7 –…

A: Integrate as general

Q: Find the solution asked using the process of Homogeneous. (16x + 5y)dx + (3x + y)dy = 0; the curve…

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Q: The equation of the upper semicircle centered at the origin with radius R in parametric form is…

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Q: dy -y2+1,ysCJse Cantial cokditian.

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Q: dy -X+Y

A: The solution to a linear differential equation of the form dydx+Py=Q, where P and Q are functions of…

Q: integrate dy/(sb - smy-bny-nmy^2

A: SOLUTION-

Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: The order and degree of the differential d³y V dy equation: 7+ is dr3 dx 3,2 7, 3, 3, 1 3,7 Question…

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Q: (ylny-exy)dx + ( + xlny) dy = 0

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Q: 2. sin3x dx + 2y cos 3x dy = 0

A: Given equation - sin(3x)dx+2ycos33xdy = 02ycos33xdy =-sin3xdxydy =-sin3x2cos33xdx             Taking…

Q: S csc“(3y)dy

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Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: A. = 2x - y + sin2t dt = 4x + 2y + 2cos2t (variation parameter). dt

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Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: Compute the differential dy for y = 7x° – 4x2. dy =||

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Q: 2- Find of y = dy dx y %3D /cos-1(In (xy))

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Q: (1,2,3) (0,0,0) 4x³y dx + (x²-25) dy-5yzª dz

A: Find the value of function using integrate Compare the given expression with Mdx+Ndy+Pdz to obtain…

Q: Compute the differential dy for y = 4x³ + 2x?. dy =0

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Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

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Q: (1 + cos 2y) dr - 2r dy = 0, y(1) = i %3D Oy = Arctan 2 O y = Arctan O y = Arctan ( 1) D y = Arctan…

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Q: 7 Find (b) x siny-ycosx-y 1.

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Q: cos²x sinx dy + (y cos³x − 2)dx = 0

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Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

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Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: Find all the second partial derivative T = e-4r cos(0) -4r, Trr 16e 'cos (0) %3D Tre = 4e -4r,…

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

Q: 5. y" – 2y' + y = 2sinx cosx y'(0) = 0,y(0) = 0 %3D | -

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Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

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Q: V4-z2 z siny dx dz dy 16 3. 16 5 0 16 0 66 0 66

A: The objective is to solve the integral ∫0π∫02∫04-z2z siny dx dz dy

Q: dy 1. sin 2ycos2y

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Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

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Q: Explain, the given differential 3x²dx + 2yz dy + y² dz is exact or not.

A: We will check whether  3x^2dx+2yzdy+y^2dz is exact or not.

Q: 1) S 2 sec y (tany – sec y) dy

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: dy = (1+3 siny)2xdx

A: We will solve differential equation using variable separable form

Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

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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.