When reduced to a linear DE of order one in z, the Bernoulli's equation dy +y dx = 3x?y? becomes dz A = 3x2 dx dz +Z dx B = - 3x2 1 +z dx dz |--3x? dz D =3x2 dx

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: Solve the particular solution of the given DE: x(r^3-xy^2+2y^3 )dy-y(r^3+2y^3 )dx=D0 @r=1, y=1.

A: We have to solve given problem:

Q: Given f(x, y) differential df = 10x?y then the total O 20xy dx + 10x² dy 20x dx + x2 O 2xy dx + x²…

A: For the solution follow the next step.

Q: Which of (a)–(c) is not equal to s(x, y, z) dz dy dx? IIT ra, y. 2) dy dx dz (a) 13 III ra,y. z) dz…

A: Explanation: Given that,  ∫01∫34∫67f(x,y,z)dzdydx   Concept Used: In ∫ba∫cd∫efg(x,y,z)dxdydzlimit…

Q: Reduce the given DE into Bernoulli's equation: - 2x*y¬ dx 3 y-4 dy_ y5 2x4 y4 dy dx dx 3 3 dy 2x* у…

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Q: Find the general solution of the following: dy 2x3 dx dy = xyi хуз %3D dy = (6e³x + 1)dx

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Q: for y = u dx dy 3/2 and u = 4x + 5 using the chain rule formula dy dy du Compute %3D dx du dx

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Q: at (x, y) = (1, 2) and z? = x2 + y² if dt dx = 4 and dt dy = 3. dt dz %3D %3D Find dz dt II

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Q: Reduce the linear DE (2xy+x² +x*)dx- (1+x?)dy=0 to standard form + yP(x) = Q(x). dx dy -2x (A +y dx…

A: The given ODE is: 2xy+x2+x4dx-1+x2dy=0

Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +y = = 3x?y? becomes (1…

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation dy 2 +y √( 1 ) = 3x²y² =…

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Q: If f(x, y) = 4x? – 8y, then the total differential of f at a = 1 and y = -2 is : O df = 8 dx – 32 dy…

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Q: Using the substitutions X = u+2, y=w+2; dx = du, dy= dw, the DE with linear coefficients (x + y-…

A: Using the substitutions X=u+2, y=w+2; dx = du, dy=dw, the DE with linear coefficients (x+y-4) dx +…

Q: Given z = 3 In(t) and y = 9t then find dy dx dy dx2 |3|

A: givenx=3lnt,y=9t2

Q: Given a+ yx = e¥ , what is 1-y dy dz 1+y dy 1+y dz 1+y el-I

A: Given equation is x+yx=ey We have to differentiate the given equation. To differentiate given…

Q: Given f(x, y) = 11x²y then the total differential df = %3D 11xy dx + 11x² dy 2xy dx + x² dy 22xy dx…

A: The function is given by fx,y = 11x2y To evaluate : The expression of the total differential df

Q: Consider the DE d?y dy + - 6y = 12x, y(0) = 1 - dx? dx 1 is a solution of the DE and determine 3…

A: y=Ae2x-2x-13 Differentiating with respect to x, we get dydx=A·2e2x-21-0   ∵deaxdx=aeax, dxndx=nxn-1…

Q: |Show that the substitution v = In y transforms the differ- ential equation dy/dx + P(x)y = Q(x)(y…

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Q: is D.E xy? dx + (x+y) dy= 0 a- linear b- Exact C- non_linear ( Explain that)

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Q: Consider the following. 2y dx — х dy %3D 2 dx dy Solve for dx dy dx Is y 3x2 + 1 a solution to 2y dx…

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Q: dy 3. + Ay = w; y(0) = 0 and A> 0 dx

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Q: The trial solution for the non-homogeneous equation d²y +3. dx? dy – 4y = (x³ + x)e* is %3D dx

A: Trial solution: - Assume the differential equation's right side, f(x), is a linear combination of…

Q: The standard form of 3dy-xydx= 3y%e*/3 by Bernoull's equation is: dx A Зе dy xy = 3e**/3,3 dx 3 x-…

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Q: Solve the DE using homogenous equations: Let: x = vy dx = vdy+ydv xy dx - (x2+3y2) dy = 0

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Q: For the given DE with coefticients linear in two variables, do the following: (x - 2y)dx + (2x…

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Q: a) Find the differential dy. y = ex⁄2 dy = ? (b) Evaluate dy for the given values of x and dx.…

A: Explanation of the answer is as follows

Q: dy +y When reduced to a linear DE of order one in z, the Bernoulli's equation |=3x?y? becomes dz (A…

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Q: Show that if you differentiate both sides of xy +4x + 2y = 1, the re- sult is (x + 2) + y +4 = 0.…

A: we have to show that the differentiation of xy+4x+2y=1 will result in (x+2)dydx+y+4=0 and then we…

Q: d?y dz? Find the two real root second order differential with for 6- + 5 dy = 6y dx O C1*e^(2x/3) +…

A: Solution:-  Given differential equation            6d2ydx2+5dydx=6y     Firstly rearrange  this as…

Q: If y is a function of x, then the equation (y - a)dx + 3ry dy = 0 is not linear + but both + and…

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Q: Solve for if y- Ina 2- y?. da MCQ3.pdf dy 2y +1 dx dy 2y +1 dx dy dæ -(2y+1)x 1 dy (2y+ 1)a TERIRS…

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Q: 2. Variable Separable eyx a) dy =D dx ey+x?ey

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Q: dx Reduce the given DE into Bernoulli's equation: = 3x³y² dy x-3 dr dy x-3 dr dy 3y2 3y? y x-3 dy =…

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Q: D. Identify the linearity of the following equations. y°dx + xdy = sin y dy 16. dzy +x- dt2 d?x 17.…

A: Given that:                                 NOTE: As per our answering guidelines, we can only…

Q: Suppose that n # 0 and n # 1. Show that the sub- stitution v = y!-" transforms the Bernoulli…

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Q: After solving for the factors of dy/dx, the equation y*[(dy/dx)^2] + 2xdy/dx - y = 0 will reduce…

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Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: Upon multiplication by -3x-4 and using the substitution Z= X¯³, dz= - 3x-4dx, the Bernoulli's DE dx…

A: To find the equation obtained by multiplication of -3x-4 and using the substitution, z=x-3,…

Q: Given f(x, y) = 8x²y then the total differential df ,2, O 8xy dx + 8x² dy O 16xy dx + 8x² dy O 16x…

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Q: Solve the given DEQS by using an appropriate substitution. a) xyy' + 4x² + y² b) (2х + у + 4)dx + (х…

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Q: Which of the following first order is linear? A. (-) == ex dy dx x dy B. (²x) ( 1 ) 4x² = ²1/ex dx x…

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Q: The standard form of 3dy- xydx= 3y e* 4x/3 by Bernoulli's equation is: dx = 3e /3,3 ху A dy B y…

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Q: Find the general solution of this DE using INSPECTION. dnda + +(x? t y?)dx = 0 2 aycdly

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Q: Reduce the linear DE (2xy +x2+x*)dx- (1+x)dy=0 to standard form dy + yP(x) = Q(x). dy 2x +y 1+x? A…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Consider the DE d²y dy dx? 6y = 12x, y(0) = 1 dx 1 is a solution of the DE and determine 3 Verify…

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation dy + y dx 1 = = 3x?y?…

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Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +yl-)= 3x3y² becomes dx…

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Q: Reduce the linear DE (2xy+x2+x*)dx- (1+x?)dy=D0 to standard form dy + yP(x) = Q(x). dx dy A)…

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Q: Obtain the solution using Integrating Factors Found by Formulas 1. 2(2y² + 5xy – 2y + 4)dx +x(2x +…

A: First we making exact differential equation then find solution.