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 2(sin-(e-3x*)- %3D V1 - e-6x2

Q: Q2: - If y = 3 sec3t and x = etan3t prove that: - dy (In3)² ,Y logy x %3D dx

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A: Using method of exact differential equation.

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Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: dy/dx of y = (x^2)cos^4(x)

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Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

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Q: 2. Cosh X y sinh x 2 cosh x sin dx dy dxxy = 1 5. (1-x)

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Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x – x³ + Iny) dy = 0, when x = 0, y = e %3D

A: Note: According to our expert guidelines only one individual question is to be answered, kindly…

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

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

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 dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

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Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e

A: exact differential equation

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…

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A: As per the guidelines we can solve 2 problems

Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

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Q: 4- Find dy/dx for y = 3[(sin-"(e-3x*)²

A: f(x) = 3arcsin2e-3x2f'(x) =ddx 3arcsin2e-3x2=ln(3)·…

Q: 4. ox x cost at cost of 3 procuct nule J cost dt + cost at [sint] + x CSLX)ま(x) = Sin x - 0 + x cos…

A: To determine ddx∫0x3 x cos t dt.

Q: 1. sinx siny dx + cosx cosy dy = 0 %3D 2. [2xy cos(x2) – 2xy + 1]dx + [sin(x²) – x²]dy = 0 3. y?dx +…

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Q: Ssin^3 (2/3 x) cos^4 (2/3 x) dx

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Q: 6) S sech? (2x- 3) dx | ex-e-x 7) S ex+e-x 8) S(eax – e-ax) dx sinh x 9) S dx 1+cosh x 10) ſ csch? x…

A: Given

Q: d?x 2 dt2 dx - 5- dt 3x = -9t2 – 1 - %3| - - dx When t = 0, x = 1, = 0, find x when t = 2 %3D - dy

A: The given differential equation is 2d2xdt2-5dxdt-3x=-9t2-1                   (1) to find x(2) with…

Q: Let y=(x to the 2nd power +3) to the 2nd power . Find the differential dy when x=4 and dx=0.2…

A: Given,    y=(x2+3)2

Q: dx 25. Integrate: S Ve-2x –1 А. Sec-1e* + С В. Sec-1е-* + С С. — Sec-1e* + С | D. —Sec-1e-* + с

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Q: dy 1- cosh x dx + (sinh x)y = e-x - 2 dy 2- - y = e*/2y3 dx

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Q: y² cos x - 3x3y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e x² - 1) dy = ((1 + x)2 -…

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Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: 9. S sec 2x dx 10. S cos x esin x dx 11. dx x+1

A: Evaluation of the above integration is

Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: y=sin-1x

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Q: 4- Find dy/dx for y = 3[(sin-(e-3x*)1² dy 3(sin-(e-3*)1* In3 2(sin-'(e-3**) 1(-6x) %3D dx V1- e-6x2

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Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

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

Q: {dy}/{dx} for y=4sin^{-1}(x^2)

A: The explanation of answer as follows

Q: 01 (test for exactness) * 4 points (siny - ysinx) dx +(cosx +xcosy) dy =0 01 (solve exact de) * 4…

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Q: 4- Find dy/dx for y = 3(sin-(e-3x²))2 dy 3[(sin-{(e-3*)i* In3 2(sin-1(e-3**) - 3x2 1(-6x) dx V1-…

A: Differentiate term by term

Q: 7 Find (b) x siny-ycosx-y = 1. dx

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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: dy 1- Find by implicit differentiation. 2- x2 + y2 = 100. 3- x³ + y³ = 3xy². 4- x²y + 3xy³ – x = 3.…

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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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Q: Obtain the particular solution. 1. 2y dx = 3x dy ; when x = 2 , y = -1 .

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Q: 2 1) (-2xy) dx + (Siny-x²) dy

A: see my solutions