1.Find a general solution of each O.D.Es. A) y" 19y = coqx +os 3 - šin 2 (3) y" + 4y/ + 6.25у — 3.125(х +1)2. (2)y" 2x 3.125(x + 1)2.

Q: B. USING GAUSS QUADRATURE WHEN N=6 5 -3 (4x − 3)³ dx

A:

Q: Show that f Va²-t²dt = a² sin-¹(2) + x√a²-x².

A:

Q: dx 2 arctan(4)- arctan (2)-a 4 arctan (5)- none of the choices 3 arctan (2)-

A:

Q: 3. Simplify x(t) = 3 cos(27200t + + sin(27200t + to the form x(t) = a cos(27200t + 0) where a and 0…

A: To convert an expression of the form Acosx ±Bsinxmultiply and divide by A2+B2=A2+B2AcosxA2+B2…

Q: 이 x 2 + .dx 2. Jordr V1-p3

A: I have explained everything with in the solution .please go through that.

Q: d. 3) [cos πx]4 %3D dx

A: 3) To find the derivative

Q: a. +4 cos x +6 sec x – 5 ) dx 2 x5

A:

Q: 1. . x + 4 dx x² + 5x – 6

A:

Q: 1² cu (u + 4)(u - 5) du

A:

Q: The roots of a d.e are -1, 2+√3 What is the solution? y = ex(c₁ cos 3x + c₂ sin 3x) + c3 cOS X + C4…

A:

Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

A:

Q: 3. Express 4xi + 5yi° + óxi* + 2yi* in simplest a + bi form.

A: Given z=4xi+5yi8+6xi3+2yi4 To express Z in a + bi Form:

Q: S(1 + nx² – x-1) dx

A:

Q: Determine the inverse of Ax) = (x+2)² -3. j(x) =-2+x+3 b. (x)=-3±V+2 f(x) =-2+ x+3 d. (x)=-3+ +2 %3D…

A: The function is given by y = fx = x+22-3                                          ..........1 To…

Q: 2 a. (1+5 ln x)³ dx fa+ b. (1+3 tan x)² sec? x dx 2x + 5 dx Vr – 3 2x3 – 5x? + 9x – 4 C. - d. dx x²…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT yyy Ü♥¯ ¶ ☆ @ ! ! ?? !! ? ?! ¿ ¡ !? S❀ W X Х Х Х Х A * ✓✓✓ DO -…

A: We have not any digital tool .

Q: 3.0 Convert the complex number 5+2 i to polar form.. ANS 5.39 21.8°. 4.0 Convert the complex number…

A:

Q: 4.a) Find d dx y = ln (2²/ n (²x + 5) b) Find dy dx y = 3√√x++2x e³x (5x²)

A:

Q: b) Prove that, S∞ (@3x+1)² dx e2x 2π 9√3

A: Let we get, Let We get, This implies, This implies

Q: Solve using of -substitution Sec (Inx) tan (Inx) dx. 4x2+x²sec Cinx) change it to exporential form…

A: Given integral:- ∫seclnxtanlnx4x2+x2seclnxdx

Q: 1. (a) Find ? ; (u²quv). ди

A: To find the partial derivative with respect to u

Q: 3) Suppose I want to use a "u" substitution to find sec² (9x + 4)dx. What should I choose for u? O…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: ¸¸ S'√ 16–16 x² d x = · (a) 16 π (b) π square unit. ©2π (d) 4π

A:

Q: 1 Evaluate Iz|= 12.0 |z| = 12.0 dz (z – 10.0)³(z² + 169)2

A: Introduction: When we study complex integration, Cauchy's integral theorem and Cauchy's integral…

Q: Solve the equation (2cos x - √3)(2 sin x - 1) = 0 on the interval [0, 2π).

A: To solve the equation 2cosx-32sinx-1=0 on the interval 0,2π. Solving the given equation.…

Q: Suppose w = 8x² + 2y², X = 3 cos(t) + 9 sin(t), and y = 3 cos(t) — 9 sin(t).

A:

Q: 1 14) Find xe™³x² dx . | 0

A:

Q: Solve by finding an I.F 1. xdy – ydx = (x² + y² }£x y - sin x 2. dy + -dx = 0 ......

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3. Solve the following: 2xdx (x²+1)2 a. b. y = f xe* dx, given y=0 when x=0 x-2x+1 dx с. d. sn (Inx)…

A: According to our guidelines we can answer only first three sub-parts and rest can be reposted.

Q: dx √x² + 2x + 2 S₁v - = In(√5-2).

A:

Q: Q2. Solve the following:- r2 1) х4 — 1 2) cot(In x) 4) | (V1- (Inx)² -dp- 3) dx 1- x3 x In x

A: Basic substitution based problem

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.