III. Homogeneous DE 1. x dy + (y – 2x) dx = 0 2. (2x + 3y) dx + (3x + 2y) dy = 0 3. 3(x2 – y?) dx + 3y(y – 2x) dy = 0 4. y dx + (x – 4y) dy = 0 5. (x2 + y?) dx + (x² + y²) dy = 0 6. 3xy? dx + (3x²y + 2y³) dy = 0,y(1) = 2 7. (x – 2y) dx – (2x + y) dy = 0; y(1) = 3 8. (x - 3y) dx + (3x - y) dy = 0; y(0) = 2 9. (x2 - 9y2) dx + (2xy) dy = 0; y(2) = -1 10. x dy + (y In y - y In x - 2y) dx = 0; y(1) = 1 %3D %3D %3D

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: appropriate method to fih general solutions of the following ations. dy -- y = x² +2x (b) (1+x²)* +…

A: In this question, the concept of a differential equation is applied. Differential Equation A…

Q: Obtain the general solution of y√(1+x^2)dx+ x√(1+ y²)dy = 0 using variable separable method.

A: solution is given below..

Q: B. Homogeneous 1. у(x*+ ху - 2у') dx + x(Зу? — ху —х?) dy 3D 0 2. (x+y sin 2) dx-x sin dy 0 3. xy dx…

A: 4. Given differential equation is                            yx2+y2dx+x3x2-5y2dy=0 ;  x=2, y=1 now…

Q: B. Homogeneous 1. у(x+ ху - 2у?) dx + x(3у? — ху- х?) dy 3D0 2. (x+y sin 2) dx -x sin dy = 0 3. xy…

A: As per our guidelines we are supposed to answer only one asked question.kindly repost other…

Q: 1. (x – y)dx + xdy = 0 2. (x + y)dx + xdy = 0 3. xdx + (y – 2x)dy = 0 4. ydx = 2(x + y)dy 5. (y2 +…

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Q: 1- xy dy + (x² + y² )dy = 0 dx 2- 2. dy – y = ex/2 3- (x + 2y)dx – xdy = 0 dy 4- cosh x+ (sinh x)y =…

A: As per the guidelines we can solve 2 problems.

Q: 3. (5x + 4y)dx + (4x + 8y³)dy = 0 5 a. 3 x² + 4y – 2y = c y2 + 7xy = c C. 5. b. x? + 4xy – 2y* = c…

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Q: 2. Obtain the particular solution A. yy' 2x(y+ 1) B. (x? + 1) dy = (y² + 1) dx

A: Topic :- Differential Equation

Q: 2y dr - y dy y (x-2y) dy, y(0) =-1 O x = 2y - e +3 %3D a y = 2r- e+3 0x= 2y-e+3 O x = 3y + 2e +1

A: Given DE is 2y dx-y dy=y(x-2y)dy ⇒dx-12dy=12(x-2y)dy⇒dx=121+x-2ydy⇒dxdy=12+x2-y⇒dxdy+x-12=12-y Which…

Q: 1. If y = V6x + 1, then what is Y? dy? %3D dx dy a. 2(6x – 1) 3(6x + 1)7 2(6x + 1) dy С. dx %3D %3D…

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Q: y=(1+2cot"x) 3 dy_ 8(1-2cot"x) dy 8(1+2cotx)° %3D dx 1-x dx 1+x? Op tion 3 Op tion 1 dy -8(1–2cot"…

A: Let's find.

Q: determine the general equation; variable separable, homogeneous, exact, non-exact DE…

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Q: Solve (x – y)dx + (3x + y)dy = 0 with the condition: y(2) = –1 O (2æ + 4y) – (2x + 4y) ln(2x + 4y) =…

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Q: 2 = x* – xy – y ,2, find the If z = {x, y) = x² - differential dz. A. dz = (2x – y)dx + (x – 2y)dy…

A: We can find the differential as below

Q: 2xy dx + (x2 + 1) dy = 0 U (2xy? + 2xy e2x + e2x y) dx + (2x²y + x e2x) dy= 0 2xy dy + (3x + 2y²) dx…

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Q: d?x dy -y = 0, dt? dt dx 2- dt dz +- z = 0, dt dx dy + 3x + dt -4y+ 3z 0; dt dx x(0) = 0, (0) = = 1,…

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Q: 1. dx+ e*dy=0 5. x(1- y)dx+(x² -2)dy= 0 5. sin2xdx+4ycos² 2xdy=0 dy_ xy+3x-y-3 dx xy-2x+4y-8 . (4y+…

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Q: Evaluate 1. Integrating Factor by Inspection a) y(x2 − y2 + 1)dx − x(x2 − y2 − 1)dy = 0

A: Only 1a) will be answered as per bartleby expert policy. Only one individual question will be…

Q: Obtain a family of solution a. (x -y ln y + y ln x)dx + x(ln y - ln x)dy = 0

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Q: 1) y" - (a + b) y' + aby = 0. Ans.: y=Ce +C e. d°y sd*y_2d°y _10d*y + +5y=0. dx dx dr dx dx Ans.: y=…

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Q: 2 Solue Bor メ= o-5 dx = y X (6) = 0 dt dy =_X yo) =I %3D

A: As per bartebly Guideline we can solve only one question.. Hope you understand

Q: dx 3x – 5y dx = 3x – y + 2z +t-1 dt dt (a) dy = 4x + 8y dt dy (b) 2x -z- 3t2 dt dz x+y+z+t? dt

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Q: (1 + Iny-) (;++i" y) dy = 0; 7. dx + y(2) = 1 Ans: In y+x+xIny-=0

A: The given differential equation is  1+lny-xy dx + xy+x22y2+3yln2y dy =0   ;  y(2) =1 Compare with…

Q: dy 1- dx e¯x-y-2 y(0)= -2 %3D dy 2- dx ylny %3D 1+x2 y(0)=e²

A: 1. ddxy=e-x-y-2,   y0=-2A first order separable ODE has the form of Ny·y'=MxRewrite, we get eyy'…

Q: 16. Given that h2) - yn+1- Yn and = xy, %3D dx then yn+1 = A. yn + hx,Yn C. hxYn - Yn B. yn - hxYn…

A: The given question has been solved below.

Q: 1.)(x + y - 1) * d * x - (x + 4y + 2) dy = 0

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Q: Solve for the solution of the Homogeneous DE: (x - y)dx + (3x + y)dy = 0 when x = 2; y = -1 a. (x -…

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

Q: 25. (x + 2y)dx + (2x + y) = 0 A. Exact B. Not Exact 26. (2xy2-3x2)dx + (x² + 2y)dy = 0 A. Exact B.…

A: as per bartleby guidelines i can solve only first 3 questions, please ask other separately

Q: III. Homogeneous DE 1. x dy + (y – 2x) dx = 0 2. (2x + 3y) dx + (3x + 2y) dy = 0 3. 3(x2 – y2) dx +…

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Q: 1. (2xy-tany)dx + (x² – xsec?y)dy = 0; y(1) = r 2. [4x°cos(xy)-x*ysin(xy)- ye" +3x²]dx…

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Q: (3y' + y)y = x (1) y' - 3x'e-y = 0 (2) Inydx + (x + y)dy = 0 (3) xy' +y = sin x+2 cos x (4) (2x –…

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Q: 2x = - (x2 + y²) (1 + 2 e) dx + 2 e7(1 -5 dy = 0 x = y In y-y In x dx O (y? – x2) dx + xy dy = 0 O…

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Q: 3. у(3x3 — х + у)dx + x?(1 — х?)dy 3D 0 4. у(2х — у + 1)dx + x(3х — 4у + 3)dy 3D 0 5. (r + sin 0 –…

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Q: 2. Identify the 3rd order nonlinear DE. 3 +x³y – xy³ = 0 \dx) d³y d²y +y dx? В. = 0 dx3 d³y d²y С.…

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Q: B. EXACTNESS 1. (xy2 + y- x)dx + x(xy+ 1)dy = 0 2. 2xydx + (y2 +x²)dy = 0 3. x²ydx + (x + 2y)dy = 0…

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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: 31. (1+ y cos x) dx – sin x dy = 0 - 32. (sin? y+ x cot y) y'= 1 33. dx – (y- 2xy) dy = 0 34. dx –…

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Q: 5. y' + 2y = 0, when x = 0, y = 2 %3D Ans. y = 2 e-2x %3D dy 6. xy +2 y– x - 2 ху — Зу+х-3 dx (у -…

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Q: B. Non-Exact 1. (y-y) dx + x dy = 0 2. (4xy + y') dx -2(x²-y) dy = 0 3. Y' = (y +1)/x 4. (y+x) dx-x…

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Q: (i) (iv) (vii) dx x2 dx = (x + 1)(y² – 1) dx 1 –x² + 2x – 1 %3D = - | dt dt dt dy dy dy = x² – 2x +…

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Q: Given: X == In(x²y - 1) y Find dy/dx. dy dx x²y-1 y-1 (E) None of these 1 2xy dy y x²y-1 dx + dy dx…

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Q: 7. The integrating factor of the non-exact DE ydx- xdy3D0 is -1/(xy). 8. The integrating factor of…

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Q: dy a) -2y dx y = 2 sin x y = sin 2x y = e2x Oy = e-2r dy b) 2y dx y = 2 sin x sin 2x Oy = e2" y =…

A: Explanation and solutions is given below....

Q: Obtain the particular solution when x = 1 and y = 1 y(x^3-y^-5)dx-x(x^3+y^5)dy=0

A: Here is the solution of the given differential equation.

Q: y") ax Zxy dy 3. x3y dx - (x + y) dy = 0. 2 dy dy LC

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Q: B. Non-Exact 1. (y-y) dx + x dy = 0 2. (4xy + y') dx -2(x2-y) dy = 0 3. Y' = (y +1)/x 4. (y +x) dx-x…

A: As per our guidelines we are supposed to answer only first asked question.kindly repost the other…

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

A: Let's find.

Q: 2- y(x + y +1 ) dx – x(x + 3y + 2)dy = 0 Reducible to Exact Method

A: We have to find general solution of given differential equation which we reducible to exact method :…