dx1 2.x1 + x2 + x3 + sin(t) dt dx2 = -x2 – 2x3 – 2 cos(t) dt dx3 2.x2 + 3x3 dt

Q: The differential equation for which sin¬ x + sin¯ y = C is given by V1- x²dx + /1- y² dy = 0 b. V1-…

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

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Q: Find the solution to the Bernoulli Equation. (3siny - 5x)dx + 2x²cotydy=D0 O x³(siny- x)2 = Csin?y O…

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Q: 1. (e)(1-e²y)¹/² dx = dy 2. cos x cos y dy-sin x siny dx = x² cos x sin y dx

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Q: dx y². dy dx dy = + 2xy = sin y,x(n) = 1 -2xcsc 2y - 2x³ cos 2y sec 2y h. i. sin 4y + (4y + C)2y π[²…

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Q: r) x²(esinx) s) e*[ln (cos x)] (m sin 3x t) e2x x COS X u) ex リこ Sm

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Q: (a) ſ x sin(2+ x²) dx (b) Sí Зи du u²+u–2 (c) ſi z dx 2 x²+x+7 (d) * x²e-3x dx -Зх

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Q: Solve the differential equation. dy y + 1 dx O In |x| – ? () = tan - ex - x + tan-'(x) = C In |x| –…

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Q: 6. [2x + y cos (xy)] dx + x cos (xy) dy = 0. 17. 2xy dx + (y? + x²) dy = 0. 18. 2xy dx + (y2 – x²)…

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

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: 4. (ye"-2y)dx + (xe-6 xy- 2y)dy = 0; x = 0 when y = 2. 5. (x+3) cos y dx - (sin y In(5x + 15)-y} dy…

A: The exact differential equation for the equation, F(x,y)=C, is written as Fxdx+Fydy=0, where, Fx ,…

Q: 2. (e2y – y cos xy)dx + (2xe2y - x cos xy + 2y)dy = 0

A: Exact differential equation

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. 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: d3x 2. Verify that sin kt is a solution of the equation in + k3x = 0 %3D dt3

A: Explanation of the answer is as follows

Q: Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

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Q: dy The standard form of the differential equation cosx =1-y sinx is dx Select one: O a. +y sinx =…

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

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

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

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Q: x-2-x-4 is x-2-x- The differential of y= A dy= -dx x2 B) dy =dx x2 none of the given choices dy=-dx…

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Q: (y² cos x – 3.x²y – 2x)dx + (2y sen x – x° + ln y)dy = 0, y(0) = e

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Q: 3. Integrate the function. (a) / Vx–1dx = %3D (b) /e2+ 2x+1 dx = (c) | (sin xcosx+ sinx cos x) dx =…

A: Hello there! You seem to have uploaded a question with multiple subparts. As per our guidelines, we…

Q: What is / - z dx? 1-x² o f- dx = -2cos-lx + C V1-x2 S- dx = 2sin-lx + C (1–x2 S-d 2 dx = 2cos-x + C…

A: 1. I=∫-21-x2dx =-2∫11-x2dx =-2sin-1x+C    ∵As ddx(sin-1x+C)=11-x2⇒∫11-x2dx=sin-1x+C=-cos-1x+C…

Q: -2-x- is The differential of y= A) none of the given choices B dy =dx x2 (c) D dy =-dx dx

A: =>d/dx (u/v) = ( v du/dx - u dv/dx)/v.

Q: 4 I. dx3, (d³y\ dy + 2- dx = sin x *+ O) + = In y. 3 II. dx dx dx d³y III. dx3 d²y , dy -2 + dx2 = x…

A: To identify which of the given differential equation is linear.

Q: -cosh(x)dx 18) St?cos(2t)dt S 2y²e»*dy 19) Sxeax+1dx dx Sx²e2*dx 20) S x-x2 ) (2?/ª x)°e-In(x²)e3×dx…

A: We have to find the integration.

Q: :Q1: Use Laplace transforms to solve the differential equation d² y - 24Y + dy + 2y = 3ex cos 2xr,…

A: Given:  d2ydx2-2dydx+2y=3excos2x      ......(1) y0=2 and y'0=5 We want to solve the given…

Q: Q1) Evaluate: (a) fe²_1_dx Inx sin ¹x 1-x² dx (b) f 1- cos dx (e) Jỗ 2sinx cosx dx (c) | Inx dx

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Q: f1-p, 01 Solve the integral equation F(x) cos px dx Hence deduce that Sin dt 2

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Q: dx —х +3у dt 13. Find the general solution dy -3x+5y dt ||

A: The objective is to find the general solution of system of differential equations…

Q: x-2-x-4 is x-2-x- The differential of y= (A) dy = dx B dy= - -dx © dy=-dx none of the given choices…

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Q: 4.) (w° + wx²- x ) dw t ( x° t w? x - w) dx = 0 ( 2x +y cos xy) dx t x cos xydy COS X

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Q: dx +4x = 2e 3 , x(0)= 5 dt (d) dx +4x = sin 2t , x(0)= 0 dt (e)

A: Laplace transferom, solve the differential equation by using Laplace transferom

Q: (d) / x² – 5x + 2 dx = (e) . (1) (f) sin(x) dr. (g) V5t2 + 3t cos t dt =

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Q: dx 2а — У dt fip dt x + 2 cos(t)

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Q: find ƒx , ƒy  . 1.ƒ(x, y) = e^(xy) ln y 2. ƒ(x, y) = cos^2 (3x - y2 )

A: Hi! You have uploaded multiple questions. As per norms, we will be solving only the first question…

Q: 4) (у-сos' x) dx + cos xdy %3D0 5) 2y(y² - x)dy = dx

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Q: 12) dy dx - = x cos (6x²), y(0) = 7 A) y == sin (u) B) y = sin(6x2) + 12 C) y = sin (6x²) + D) y -…

A: In the question we have to solve the differential equation. Bartleby's guidelines: Please post…

Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

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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: dy + ydx = 3x²y?dx, %3D

A: Let's find.

Q: 3n 2n TE S. (sin x + cos y)e dx dy dz A. 2n(e2n + e3) B. 2m(e2 – e3") c. 2m(e + e2") p. 2n(e- e")

A: For the solution follow the next steps.

Q: x-2-x-4 The differential of y=- -2 - x -3 A dy =d xp - B dy= - -dx dy =-dx D dy: -dx is

A: we have to find

Q: 1. 2sin?2t dx = cos x(1 + cos 2x)dt 2.3e-3y dx – ee+xx-2dy = 0 3.x*ydy — ху?dx + 3ydy - 2xdx %3D 0

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Q: Obtain the solution to the differential equation: y cos x(2y sin x+ 1)dx+ (sin x- 2y cos²x)dy = 0-…

A: The given differential equation is: y cos(x)2y sin x+1 dx+sin x-2y cos2x dy=0

Q: h'(x) = cosxcot(sin^3x)+cosxsinx ⠀ h(x) = sin(x) -2 (cos(t³) + t)dt

A: Applying Leibniz's rule

Q: 11. (e* sin y – 3x²)dx + ( e* cos y+ |dy = 0 12. (2x + 1+x?y? ) dx +( -29) dy = 4 - 29) dy = 0…

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Q: x-2-x-4 is x-2-x-3 The differential of y= A dy =dx B none of the given choices dy = --dx D dy =-dx…

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Q: a) Find the differential dy of y=x2+2x+5. (b) Evaluate dy for x=3, dx=1/2. (a) dy=????????? dx (b)…

A: GIVEN THAT y=x2+2x+5

Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…