TT Q3(a)- P.T B(m, n) = 2 [? sin2m-10cos2n-10 d0. b. Also verify part (a) with counter example.

Q: dy 13 %3D - dn Solve this by using Bernoullis eajuation?

A: Given differential equation is: dydx=y(xy13-1)dydx+y=xy141y14dydx+1y13=x                         (1)…

Q: Approximate (a) cos 0.8 and (b) cos 1/2 using the linear approximation technique

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Q: Integrate -- | cos 5xcos x a) 0.5 b) c) d) 2

A: We can use the trigonometric identity, cos A cos B=12cosA+B+cosA-B . Use the integration formulas,…

Q: 2cos'z = COS T Select all correct solutions.

A: Follow the procedure given below.

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: (iii) 1 dø -sin²Ø Hint: may start with de (T(1/4)} /2 Vcose to obtain the result

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Q: fx) = Зх - 4 at (4, 2) d y=x In x at (0, 1) sin3x y = 4 at T 2

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Q: dx Integrate by trigonometric substitution: .2 4x² -9 2

A: Given integral :

Q: (e² sin*(2r)' 21² +1 , y = In

A: Use the lograthim rule of derivative and than with the help of chain rule calculate the derivative…

Q: T T 68. y = sin 3 + 4 %3D -

A: Given data:     The given expression of the function is: y=sin(-πx/3 – π/2)+4.     (a) The general…

Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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Q: Solve the equation siny(X+siny)Dy+2x²cosydy=0

A: Consider the provided question, sinyx+sinydx+2x2cosydy=0sinyx+siny+2x2cosydydx=0…

Q: Find the solution. (Dª+2D3 + 10D2)y =0. @y = c,e-+czxe¯+e"(e,cos3r +c,sin3x) y = (c,+c,)x+e*(c,cos3x…

A: To solve the given Differential equation.

Q: / – 9x* sin²(7y") = 9x* cos²(7y/") What is y(4) if y(0) = 8? %3D %3D

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Q: Find d-/dx² at the given point without eliminating the parameter. x=0+ cos0 and y=1+sin0 ; 0 =a/6,

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Q: 1. In interval 0 sx< 2n, how many values of xsatisfy the equation 3sin2x + sinx -2 = 0? (a) 0 (b) 1…

A: Given query is to find the number of value of x which setisfy the expression in the interval of…

Q: y=cos(4x) /cos22x-4sin2x cos2x differentiate?

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Q: Q2: Solve the DE y' – 4y = sinx.cos2x by undetermined coefficients method.

A: The given differential equation is                                    y'-4y=sinxcos2x  ......(1) The…

Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

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Q: a. The velocity of a car in meters per seconds travelled from its origin is given by v(t) = In (t2 +…

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Q: derive 8t sin t (d) s %3D cos t t5

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Q: 1. Use a substitution to find (6a2 + 2)e*+# dx showing working.

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: cos"(siny) dx dy = %3D

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Q: fCx) at c0,2) で +x + co.2) 2. メ 2/3

A: Given curve is fx=23x2+x+2. To find the equation of tangent line and normal line of the curve at…

Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

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Q: i. Jsin xcos 2x - sin 2x cos xdx

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Q: (D5+3D + 4D³ + 32 cos (2a) + 3e 12D²) y = 16 sin (2x)

A: The given differential equation is…

Q: S cos³y sin³y dy 3.

A: Given,            ∫cos3ysin3ydy

Q: cos e de =_ %3D • 2 • -T • 6

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

Q: 6) F Sin12y Cos’ y dy

A:

Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

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Q: 5. J sin42x cos22x dx.

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

Q: Q1 Evaluate 1, where: -So I = -3x cos 2x dx

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Q: A particle is moving along a line so that at any timet, where 0 st sn, the position of the particle…

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Q: Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x +x?

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Q: check by differentiation that y=5COSE 4 Sint is a solution to y"ty=D0 by finding the terms in the…

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Q: 8 cos (2r² + 2y²) dy dr Hint You could take a cab to the pole.

A: Given the integral is ∫02∫04-x28cos2x2+2y2dydx

Q: Solve the DE when all conditions set to zero. (D² + 4)y = sin²2x

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Q: Solve the eaation on the interval. 2sin Đ =3(cos o t D

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Q: (D² – 3D + 2) y = 14 sin 2x – 18 cos 2x

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Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

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Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: dx If x² – 2x – 4 is solved by trigonometric substitution, the resulting integrand is?

A: The integral function is ∫dxx2-2x-4dx

Q: (D3- D2)y = cos2t a. y, = -cos2t +sin2t 10 20 b. y, = - cos2t -sin2t 10 20 c. p =cos2t- sin2t 10 20…

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Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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Q: Using the Method of Undetermined Coefficients, give an appropriate guess for yp. y(4) + 9y" =…

A: Given the DE is y4+9y''=cos3x+4x2. Guess the particular solution of the DE.

Q: Solve the fo llowing D.- E y + y tan X Cos X %3D

A: