Evaluate using Algebraic Substitution: Vy5–1 dy O {(Vy³ – 1 응(Vy, - (Vy – 1 tan-1 Vy – 1) + C - | 27 1- sin-1 Vy –- 1) + C tan-l Vy – 1) +C | None of the choices. Please refer to my solution.

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

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A: we have to show that the following

Q: 2. If f(x, y)=x² sin y-y cos.x-xe - ye" +5x°y°, show that ô²f _ ô²ƒ ôxôy ôyôx

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Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: sin, ifx T 2л

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Q: find general Solution (D²+6D. Sin 4X to

A: Given differential equation is : D2+6D+16y=sin4x To find the general solution.

Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

Q: 3. What we want to do next is write (x + jy)as Relº where R = (x2 + y² ) and tan-1(0) = (2)

A: If you have a complex number z = r(cos(θ) + i sin(θ)) written in polar form, you can use Euler's…

Q: 28) To evaluate S dt we could use the substitution a) t = sin(u) b) t = tan(u) c) t = sec(u) d) t =…

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

Q: () -1 -3y If f(x, y) = tan %3D then find fr .

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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: f (t) = 4 cos(4t) – 9 sin(4t) + 2 cos(10t) (As* + Bs3 + Cs² + Ds + E) Fs) Fs4 + Gs3 + Hs² + Is + J

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Q: H 2= x? tan y/ at (lo1) %3D Ex by

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Q: x’y? If z , show that x=+ y- 3z x+ y ôx ây a²z ô²z = 0 if z= Tan 2.xy x² – y? Show that âx² ' ây²

A: A detailed solution is given below.

Q: = cos(x + y), when x = 0, y = " %3D

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A: We have to find out

Q: Find Duf at P. 3 f (x, y) = sin(3x – 4y); P(4,3); u = j - - NOTE: Enter the exact answer. Duf = |

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Q: If u = tan -1 x- the value of x2 +y?+xy du at x = 1 and y = 3 is

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Q: is a solution of y' y sinx. -COSX Select one: O True O False

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Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

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Q: 1. Find y' of tan(x²y*) = 3x + y² Answer: y': 3-2xy* sec²(x²y*) 4x² y3 sec2 (x2y4)-2y

A: We will solve the problem

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A: Given function is fx,y=tan2x-3y

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A: Given:         limy→12π2y-πcos y    Let   π2-x=y, ⇒π-2x=2y      As y→π2,x→0

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Q: y = cev2z + Cze + C3 cos(v2x) + C4 sin(/2x) + Czev3z + Cge + c7 cos(/3x) + Cg sin(/3x)?

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Q: Q1:-/ Verify by direct substitution that y, = epx cos qx and y2 = ePx sin qx , are solutions of the…

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Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

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Q: If f(x, y) = x³y + cos(x) then (fa, fy) = (3xy - sinx, x³). Select one: O True O False

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Q: Solve the equation for x, where x is restricted to the given interval. y = 3 tan 2x - 1, for x in…

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Q: f (t) = 4 cos(4t) – 9 sin(4t) +2 cos(10t) (As* + Bs3 + Cs² + Ds + E) Fs) Fs4 + Gs3 + Hs² + Is + J

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Q: State the trigonometric substitution appropriate to the integral: fx*(x² - 16)² dx 3/2 | A. x 16 sec…

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

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Q: ch, choose its equation from the following. = sec (x+²) = y = cot (x + ²) 4 v=2 tan x 2 y=-csc x 1 T…

A: we have to find the graph

Q: a²f Compute , and Je Te дхду f(x, y)= x'y² – sin 2+ xe" əx' əy

A: Explanation and solution is given below....

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Q: [x 2. x tan --yjA +xdh = 0; when x=0, y=z/2 ......

A: Given differential eqution  x tan2yx-y dx +xdy=0      ;  y0=π2

Q: Find Duf at P. 3 4 f (x, y) = sin(x – 5y); Р(5, 1); u = i и %3 - - NOTE: Enter the exact answer. Duf

A: This is a directional derivative problem

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Q: z) tan(y2 + %3D

A: Given that, wx,y,z=tany2+4zx3x=r2t2y=r2tz=rt2 Then we get,…

Q: If y= tan x, prove that y 2(y² +1)(3y² +1).

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

Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

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Q: Given G(x, y) = y* sin(2x) + x2(y10- cos(y?))".Find Gyyxxxy- a. - 192 sin(2x) Ob. -192 cos(2x) OC. -…

A: Given:   G(x,y)=y4 sin (2x) + x2 y10-cos (y2)7       ....(1)To find:  Gy y…

Q: Hf sin x = A + B cos 2x +C cos 4x, then A = %3D C =

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Q: d (a) Show that -(sec x) = sec a tan r. d.x (c) Differentiate y = In(sec + tan x). •ㅠ/8 (d) Hence,…

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Q: Find the clerivative of Y. a) y = Sin3x t cos3 x %3D b) y = tan? (x³) c) y=4 sec (5x)

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Q: Q1/ Sketch x1[n] , x2[n] , x3[n] where : x1[n] =Sin(rtn) , x2[n]= e^( n), x3[n]=x1[n] - x2[n]

A: Graph of sin(πn)

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Q: (2D – 5)y = sin 2x – 7 cos 2x -

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