13. (D² -1)y = x³ sin 3x

Q: 4 b. [√x ln xdx, 1 4 ㅠ C. fx√4-xdx, d. fx sin (2x) dx. 0

A: Solve the following

Q: . (4x³y5 sin 3x + 3x*y5 cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A: See the solution.

Q: ( 2x – sin y) dx – (x cos y) dy = 0 -

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Q: 1) ex-ydx + sin y sec x dy = 0

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Q: [y²e + √elnx dy-(xy) sin² ( * O) + (---) (-) sin² tan² ,dx ey+Inx dy y(In2x-lny) -ex. dx = 0

A: We can solve this using substitution method of ordinary differential equation

Q: 16 4+x² dy when y = Find 4 – x² dx dy dx

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Q: 5y + sin y = x²

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Q: 5-(1+x')(dy-dx)= 2.xydx;

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Q: 4 Find dx for y = - +7 sin x. X

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Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: б бу-гу2 -14-292 y dx dy

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Q: If y = (3x)sin (2æ) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: (solve exact de) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xye )dy

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Q: (- + 2 cos 2x ) dx + (- - 2 sin 2y ) dy = x2

A: You have asked multiple questions in a single request. As per our honor code, we will only solve the…

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: 17. (Vx-x)dx (1-x²) dr 18. 19 o. Sy² dy 20.

A: Given problems:-

Q: 1. Solve (cosxcos y+2x)dx-(sinxsin y+2y)dy=0

A: (cosx cosy + 2x)dx - (sin x siny + 2y)dy = 0 => cosx cosy dx + 2x dx - sin x siny dy - 2y dy = 0…

Q: 3. If y = (5x)sin(3x), then dy dx ||

A: Given the function y = f(x)

Q: (e² sin³(2r) (d) y= ln 2x2 + 1

A: Given, y=lnexsin32x2x2+1 derivate both side and find dydx dydx=ddxlnexsin32x2x2+1…

Q: у (9х — 2у) dx - x (6x = y) dy = 0 -

A: Given:- y (9x - 2y) dx − x (6x — y) dy = 0 To find:- Solve given differential equation when x=1, y=1

Q: dy 2 3 ...2 C05X +sinx...y.-(4x+5). y. ---

A:

Q: 7. 2r tan y dx + sec² y dy = 0

A:

Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

Q: 2 1. Z =- 1+x2 ; d²z/dx?

A: z=21+x2

Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: 2. (2.xy – sin x)dx + (x² – cos yldy =

A:

Q: 1. If y = sin x² x =²), ex find dy dx

A: Given y=sinx2-xex To find dydx

Q: (3– 3cos5x)} (3x² +2x-7)² (e - sinx +3x) y= Find dy/dx if

A: That's computational, take a careful look.

Q: 3 sin(3x) 2cos (4y) dy dx (-)= 3 4

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Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

Q: 10 5. Find dy/dx if x tany + y" Sec x = 2x.

A: 5. Given: x2tan y+y10sec x=2x Differentiate both sides with respect to x: ddx[x2tan (y)+sec(x)…

Q: 4. Evaluate V9-x² sin(x² + y²) dy dx

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Q: dy 4. Find at (- 2,0), if 3x² +2x²y² +sin y=12+2y. dx

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: B) Find dx dzy and if x = sin 3z and y = tan23z dx2

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Q: 2. sin y(x + sin y)dx + 2x² cos ydy = 0

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Q: 8) a) Find dy/dx if: e3x = x+y b) Differenctiate y = (sin r)"

A: We know that general derivative of d(xn)/dx is nxn-1. And derivative of d(sinx)/dx = cosx  d(lnx)/dx…

Q: 2. If xy+Y find the value of dy dx2 5- at the point Co,-1)

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Q: х2 9 dy + sinx - у %3D0 dx

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Q: 3. a) If y = 6x - 5x +7x +2x – x+10, find dy at (2,3) i. dx d'y il. -at (1,-5)

A: See the attachment

Q: 3 -V7 dz dy dx dy dz dx

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Q: 1. fx³e*/2dx /4 2. S*x sin 2x dx

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Q: Obtain the general solution of x^2 d2y/dx2 -2xdy/dx+2y=sin(lnx)

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Q: 3) Find d²y/dx² at the point (1, 1), if x6 + y6 = 2.

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Q: 3. Find dy dx y= 3 Sin.

A: Find derivative

Q: (2xsinx +3 cos y)dx-3x sin ydy 03 ....

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Q: сл/4 сл/2 30. cos(2x + y)dy dx )л/4

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Q: I sin 2 dy dx (x² – y) dy dx 5. 6. x? – y² dy dx 8. L ellyt dx dy 7.

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Q: π/3 7. Sp² sin 0 de dp π/6 8. (2-y)dy dx 9. 5/¹¹² x cos y dz dx dy

A: Since you have posted multiple sub parts question in this question which are not interlinked so i…