From (1) (Y + x*y +2x2) dx +(x + 4×y" + ® y³) dy = 0 - ydx + xydx + 2x²dx + xdy + 4xy"dy +oyy =(Y.dx + xdy) +(x³y dx + 4xy* dy)+ 2 x²dx + ®ydy We have dlxy) = Xdy + ydx = Ydx + xdy , than d(xy) + xy(x²dx + 4y3dy) + 2 x°dx + 8 y³dy=o 43) Wle have d(x3) dx = 3x2 > dCx3) 3x?d x -d(x3) = x²dx Smilarly (y") = 4y =) d(y") = 4y%dy d(y) = yay (5)

Q: y(x²-1)dx + (x³+8y-3x)dy =0  when x=0, y=1

A: Given: 3y2(x2-1)dx+(x3+8y-3x)dy=0initial condition is x=0,y=1

Q: ind dy/dx. y= -3x square root of 1-4x^2

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: 16 (1.) 2XInX 2 dy/dx (2. if 4 = cosh 2 JX +1 %3D 213 dx (3.) 4+x2

A: Question 1 is solved by substitution method. Solving other questions are against the policy of…

Q: Inx+ 1 dy If y = then %3D 2x3 - 3x' will be dx (2x – 3x) + 1) – (In x + 1)(6x² – 3) А. (2x³ – 3x)² -…

A: Use the formula of differentiation of fraction of Two functions in same variable.

Q: 6. (6x – 3y + 2) dx - ( 2x - y– 1) dy = 0 ans. 3x - y + C = 5 In | 2x - y + 4|

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Q: Compute dy / dx and d2y / dx2              x 2 - 4y 2 = 8

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: 1. 2d2y/dx2 - dy/dx + y = 0 2. d2x/dt2 + 4dx/dt + 4x = 0 3. 2d2y/dx2 -3 dy/dx +2y=0

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Q: dy If y = (5x + 1)(2x +In x), then will be %3D dx (5x + 1) +) + 5(2x+ In x) A. -1 B. (5x+ 1) - 2. +…

A: The given problem is to find the derivative of given function y=(5x+1)(2x-1+ln(x)) , we can use…

Q: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

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Q: Find dy if y2T+4+ In(x+2)= xy3 dx y - 2Vx+4 2yvx+4 -3xy 2x+4 2yvx+ 4 y -2 2yvx +4 - 3xy- Vx +4 2yvx…

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Q: Evaluate the integrals

A: Given I=∫01∫03-3x∫03-3x-y1dzdydx

Q: dy/dx and d^2y/dx^2

A: Here; x=e-7t+2 .................. .......(1) y=6e2t+e-3t-4t   ......................(2)

Q: /2x- xy dydx = 0,

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Q: 2. (8x³cscx++y+ 2y²sin²x)dx+ (x+2xy – ysin2x) dy=0

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Q: 4. 5. (3t dt)/((t² + 3)) dx/ (3x + 1)

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Example 3: Estimate S, x² dx with n=4 by Midpoint Method. Solution:

A: Here first we will divide the integral range into 4 equal parts and then we will calculate the…

Q: Evaluate the integrals

A: The given integration is: ∫03∫09-x2∫09-x2 dz dy dx Here first to solve the inside integration with…

Q: If y = u² + 6u - 2 and u = 4x² + 8x + 1. Find dy/dx.

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Q: 8. 5x* + -- * ) dx +2 (x³ + In x – e*) dy = 0; y (1) = 0 %3D

A: Differential equation solved by using integrating factor

Q: Solve the particular solution of 3y(x^2 - 1)dx +(x^3 + 8y - 3x)dy = 0; when x = 0, y = 1

A: The given differential equation is 3yx2-1dx+x3+8y-3xdy=0. The initial condition is x=0 when y=1. The…

Q: (A) Evaluate / (4x – 5) (4/x + 4x) dx. x² + 3x - 6 (B) Find dy -, if y = 3 -)4 when x = 1 %3D dx

A: *we have to perform integration operation in A & differentiation operation in B.

Q: find dy/dx 3x² +5y'x² +4/y, a) x² +4x,/y-5y² = 3 (ans.: 2x 10x'y- Jy

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Q: 1. (3x – 2y + 1)dx + (3x – 2y + 3)dy = ( -

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Q: 1. (2x – 3y) dx + (2y – 3x) dy = 0 - -

A: According to our guidelines we can answer only three subparts of a question, or first question and…

Q: Find dy/dx.  X4y1/3 + e7x - y = (x3 - 11)6

A: X4y1/3 + e7x - y = (x3 - 11)6  dy/dx = ?

Q: Find d^2y/dx^2 at (-1,-2) if 3x^3-2x^2+x = y^3+2y^2 +3y.

A: Given function is: 3x3-2x2+x=y3+2y2+3y Let us consider: y'=dydx ; y''=d2ydx2 Differentiating both…

Q: (3x + 7y)dx + (3x + 6y)dy = 0 (2x² + 8xy + y²)dx + (2æ² + xy³/3) dy = 0 %3| (2x – 5y)dx + (2y+ 2x)dy…

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Q: (2,5, – 6) | 16x dx + 4y dy + 2z dz (0,0,0)

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Q: Find the particular solution from y(9x-2y)dx-x(6x-y)dy=0  when x=1/3 and y=5/2.

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Q: 10-4z .5-2x-y 6z2 dz dy dx

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Q: (2xy + x²)dy + (2xy + y²) dx = 0 A2 (3x² + 2xy) dx + (x²) dy = 0 *A3 (3x²y³ + 3 sin x + 4y) dx +…

A: Disclaimer: SInce you have asked to solve only question 3, this question has been solved only.…

Q: 4) [cos(2y) – 3x²y²]dx + [cos(2y) – 2xsin2y – 2x³y]dy = 0

A: Exact Differential equation

Q: find dy/dx: (x+y)3+ (x-y)3=x4+y4 ?

A: The given equation is x+y3+x-y3=x4+y4. Find the derivative dydx using implicit differentiation as…

Q: Find the general solution of dy (y2 + 4) In x In(y2 + 4)"* %3D dx

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Q: (4) (2xcosy+3x²y)dx+(x³ – x²siny-3)dy=0

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Q: Find the solution of dy/dx = (-x^2/y^2) + ( 1 / ( 3y^2 (x^3 + y^3)^2 )

A: Given: dydx=-x2y2+13y2x3+y32

Q: 1,- X73X+2 dx (x+リ) Izafhinx dx Ax. Iォfュース alx dx X43X+2 X+1

A: Since, you have posted multiple, we will solve only first part. If you want solution of other…

Q: dy 4. if y = csch-1 2º . de 2x+2 dx . 5. J2-2x+1 x² –2x+1 dy 6. dx if y = (1+ x²)etan-1x

A: Given; 4. y = csch-12theta 5. Integration of the term (2x+2)/(x2-2x+1) 6. y = (1+x2)etan^(-1)(x)

Q: 1. Non-Exact DE (4x² – 4xy + 3y² + 2x – 3y)dx +x(2x – 2y + 1)dy = 0 -

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

Q: 1- [(2x – 5)/3x – 1) dx | 2- S S(x3 – 10 + 3y² dy dx

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Q: (2x+ 3y) dx + (3x-y+5) dy

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Q: Find dy/dx of 10x - 18xy2+10y3 = 48 9y-20x 3 (бу? -5ху) dy !! dx 9y-20x dy 3 (буз - 5ху) %3D dx dy…

A: topic - implicit differentiation

Q: 3. (6x + y²) dx + 2x - 3y) dy = 0. ANS. 3x + xy² ya:

A: Here we have to solve the differential equation.

Q: /25-x2 V25-x2 -y2 1 dz dy dx -/25–x² -V25-x² -y²

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Q: 2. (2x + 3y + 1)dx – (4x + 6y – 1)dy = 0 -

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Q: (1-xy)^(-2) dx + [y^2 +x^2(1-xy)^-2]dy=0; when x=4, y=1

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Q: (b) Integrate x-³e-l/a², dx

A: Here we can find the answer as below.

Q: 2. fizə] ycos (xy)] dx + [2xe2y - xcos (xy) + 2y] dy = 0

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1. y = x3 – 2x² + 3x – 5 - - dy 3x2 – 4x + 3 - dx

A:

Q: 1. (2xy + x²)dy + (2xy + y²) dx = 0 1000 A2 (3x² + 2xy) dx + (x²) dy = 0 2. *ALA 3. (3x²y³ +3 sin x…

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