find /x – x² - dx xV4x – x² dx 9. 10. х dx dx 11. 12. xV7 – x² xV7 + x² Vx² (4 x² 4 dx 13. 14. х sin 4t dt cos 3t dt 15. 16. 17. fz05 r cos-1x dx x tan¬1 x dx 18.

Q: Find the general solution. 1. (2xy-3x2)dx + (x2+2y)dy=0

A: According to company rule we can answer only first question and rest can be reposted

Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: B. By miscellaneous substitution (VE+1)dx dx 1. S 2. S: 3 cos x+2 sin x-5 XA +

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Q: find tu general Solution of: 2x a) y"-y' - 6y + Cosh = e b) y! -Y = Cosh 2x + Sinh x

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Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

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Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

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Q: Obtain the General Solution : • tan'ydy : sin xdx e • COS "x sinx dx o • (3t sinix) dx = sin 4x dy

A: Solve above differential equations.

Q: 1. S (5x-12) dx 2. S x³-6x² +8x 3. S -(3 cos² 0 +8 cose-12) sine de cos³ 0+7cos² 0+ 12 cos 0 dx…

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Q: 1. sin x sin ydx + cos x cos ydy = 0 2. 3 ydx = (3x + 1)dy 3. (х — 2 у)dx + (2х+ у)dy %3D 0

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Q: Find the solution. (y - x- xy cotx) dx + x dy = 0 A) xy sinx = c + sinx - xcosx B) xy cosy = c+ sinx…

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Q: 3. Find a result by using exact for a. cos(x + y) dx + (3y2 + 2y + cos(x + y))dy = 0 2)dx

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Q: 1) = sinx + ytanx dy dx 2) x = y + x sin? 3) Prove that (2xy – 9x2)dx + (2y + x² + 1)dy = 0 is…

A: 1   dydx=sinx+ytanx        the equation can be written as standard form        dydx-ytanx=sinx…

Q: 2- X. Sin (5X) dx: Cos (SX) X Sin (SX), Cos (SX) XSin (SX) XSin (SX) Cos (SX) 25 25 25

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Q: 2. Evaluate a. [x'(2x° +5)' dx b. dx V1-7x c. [cos 3xsin 3xdr d. sin* 6x cos 6xdx e. [t* cos(2r'…

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Q: dy : y4 — e²xy³ = 2 sin(x + 3y). dx cos(x+3y) + y²e2xy³ 2y³ +3[cos(x+3y) + xy²e²xy3] cos(x+3y) +…

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Q: 6. (5x*y+ 4x³y³) dx + (3x³ + 5x*y²) dy = 0 7. 3y4 dx + (4xy³ + 5x¯2y+) dy = 0 8. (2xy? + y + 2xy cos…

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Q: Choose the correct steady-state oscillation of y" + cy' + y = r(t) with C>0 and r(t) = sin(4t) . 4c…

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Q: Find the differential dy of the given function. y sec² x x² + 2 dy sec²x(x²+2)tan x-x (x² + 2)² dx X

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Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: 1- Evaluate: 2y sinx dy dx อน 2- If u = x² + ey², x = sin 2t , y = cost² find Ət

A: Above question is solved.

Q: solve the differential eq + 2x) dx = = (2y \1+x²y² |dy 1+x²y²

A: The given differential equation is: y1+x2y2+2xdx=2y-x1+x2y2dy

Q: a. Find the General and Particular solution of dy/dx = −8 sin 4x ; y = 6 when x = 0

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Q: dx (2tx +x+ cos t) + (-sin x +t² +t)- = 0. dt %3D

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Q: 2. gxc2x2+3 dx Selast & du 니 get x in terms of u ut 2x2 +3 4-3 = ㄹ x² 4-3 x = 이들 4-3 z soke har x…

A: Given ∫x2x2+34dx

Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

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Q: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

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Q: | (3x – 2x + 1) dx 5. |(x - 1)° dx 6. 7. (x² – x*) dx 8. cos x dx /2 I sec' x dx 9. dx 11. (4 – 2x')…

A: 5. I=∫13(3x2-2x+1)dx =∫133x2dx-∫132xdx+∫13dx =3∫13x2dx-2∫13xdx+∫13dx =3x3313-2x2213+x13…

Q: π/2 g(x) = 2x + 4 sin² x g(t) dt. - n 0

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Q: 3tanh 1x 1. S 1-x 2. S cos x dx sin x 1+sin?x e*dx 3. S Vezx-16 4. Find for y = e3* sech x dx x dx…

A: 1. The integral given is  ∫3tanh-1x1-x2dx......................(1) Substitute…

Q: find (x² – 2x + 1)e²* dx dx 9. 10. fun tan - y dy y dy 11. 12. sin- x sec² x dx 4x sec2 2x dx 13.…

A: Hello thank you for the question. We’ll answer the first question since the exact one wasn’t…

Q: Find the solution. (y - x+ xy cotx) dx + x dy = 0 xy cosy = c+ sinx - x secx B) x siny = cx+ sinx -…

A: The given differential equation is y-x+xy cot xdx +xdy=0. The integrating factor of the linear…

Q: zln x dx 2) S 3 cos3 x sinó x dx 3) 12.1 dt 13. 3t + 2

A: Explanation of the answer is as follows

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

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Q: Find the differential dy of the given function. y sec² x x² +2 dy = sec²x(x²+2)tan x-x (x²+2)² dx x

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Q: 4- Find dy/dx for y = 3l(sin-(e-3x')1² dy 1(-6x) = 3(sin-(e-3*" )I* In3 2(sin¬1(e¬3x²) dx In3…

A: Given y=3sin-1e-3x22

Q: dt dx 3. 6x – x² 4. sin xV1 XN Cos xdx 3x 5. 1-2e3*) 6. dx

A: We solve only 4th question.  Let 1-cos(x) =t

Q: 3. (sın 2y - 2x cos 2y) dx +( 2x cos 2y + 2xsın 2y)dy=Dd X = 2, Y = TT when

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Q: Intergrate dy (2y-x) =In Co)

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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: Use Euler method to estimate the solution of 1 sin 5x - 5e cos 5.x, dx with initial condition v(0)=0…

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Q: Find the differential dy of the given function. sec² x y x² + 2 sec 2x (2x²tan x + 4 tan x-2x)…

A: This question is based on quotient rule

Q: find / sin³ x cos³ x dx cos³ 2x sinº 2x dx 11. 12. cos² x dx sin? x dx 13. 14. 16. 7 sin y dy 7 cos'…

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Q: 1. S(e2x – 1)3 dx 3. S sin 2x (sin®x + 1) dx 2. S(x6 – 3x²)ª (x5 – x) dx -

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Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

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Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

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Q: 4- Find dy/dx for y = 3(sin-(e-3x*)2 dy 31(sin-(e-3*")r* In3 2(sin-'(e-3x")- dx 1(-6х) е 1 - e-6x2

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