Q4/ Find only five of the following: 1-[t cos at 2-f(6 sin 2t – 5 cos 2t 6. 3+2S 3-[( 3 t5 – 2 t3+ 4 e-8t) 4- - 2S-3 9 S2-16.

Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: Evaluate [(1 +x-3 + sin4x)dx -2 cos4x X - + c 4 0x-- cos4x + C cos4x O 2x- 4 0 4x-두-5t +c cos5x + c…

A: As we know that the integration of : ∫fx±gxdx=∫fxdx±∫gxdx ∫xndx=xn+1n+1+c ∫sinxdx=-cosx+c

Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

A:

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

A: To find the value of the given integral ∫sin2xcos2x1+3cos4xdx using substitution

Q: Locate the approximate root of cos(x) – xe* = 0 using fixed point method, stop with the iteration if…

A:

Q: What is the particular solution of the function 3e" sin 5x – cos 5x? A cos 5æ + Bsin 5x + C'e" cos…

A:

Q: Consider the following IVP: y +y = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

A:

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: [10 sin(2x) cos(2x) √ cos²(2x)-5 dx O a. 5 (cos² (2x)-5) ³/5 + C 3 5 O b. -(cos² (2x)-5)³/2 + C OC.…

A: To evaluate the given integral.

Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

A: A detailed solution is given below.

Q: Find L {(2- t) (5 cos 3t 1)}. - 5(s²+9) (s² –9)² 10s - 82-9 5(s2-9) 10s - - s2 s2+9 (s²+9)² 10 82…

A: As we know from the Laplace transformation; 1). La·ft+b·gt=a·Lft+b·Lgt 2). Ltnft=-1ndndsnLft And…

Q: Find L {(2- t) (5 cos 3t - 1)} - 1)} 5(s² +9) 10s s2-9 (s2 –9)² 5(s²-9) 1 2 s2 10s s2+9 (s²+9)² 2. 1…

A:

Q: Q No 4) Integrate S cosec³xdx . AND also Find F sin10xdx

A:

Q: 16. If 2 sin 2x s 3 cos2x and 0s 2x then x=

A: Given : if 2sin2x = 3cos2x and 0≤2x≤π2 . then we have to find the value of x.

Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

A:

Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

A:

Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: S cos(3r)(sin(3x) +5)10 dz Select one: (sin(3z)+5)" 11 +C O (sin(3r) + 5)"+C (sin(37)+5)" 33 +C…

A: Consider the integral: I=∫cos3xsin3x+510dx……1

Q: Find the iterative scheme for the root of equation sin x-3x +1=0 by Newton-Raphson method. O a. None…

A:

Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

A:

Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…

A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx

Q: What is 1-1] 2s – 3 2s +2 A. -2 cos 2t-3 sin 2t В. sin 3t V3 cos 3t 3 cost--sint 2 C. D. -2cosh 2t…

A:

Q: Find L{10) } s(s²+16) 1+cos(4t) 16 1-cos(4t) 4. 1-cos(4t) 16 1+sin(4t) 4 1-sin(4t) 16

A:

Q: - Find all solutions for 4 cos x+V3 = 2 cos x if 0<x<2n. %3D

A:

Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: sin(6x) cos(4x)dx% = %3D (b) ÷( + ) Nin (6x) cos (2x) COR +c 2. 2)+ (e) None Cos (2x) Cos (10x sin…

A:

Q: я/4 4 sin (4t) dt. 9- cos (4t) Evaluate the integral я/4 4 sin (4t) dt%3D 9- cos (4t)

A: Use integration by parts

Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

A: Given

Q: 4) z = (4 + j3)sinh(3+j)+cos(3-j2)

A:

Q: Find the general solution 6. y"+4y' = sec2x Solution 6. y=c, +c, cos 2x+c, sin 2x+ 16 sin 2x -In(sec…

A: Given differential equation is y'''+4y'=sec2x We have to find the solution of the given differential…

Q: Find L {(2 – t) (5 cos 3t – 1)}. 1 g3 10 + s2 +9 - - s2 s(s²+9) O 1 s3 10 + s2 -9 2 - - 8(s2 –9)…

A:

Q: Q3- Find: 1- Sv2 + sin3x . cos3x dx. 2-5* dx x5-2x sin 2x 2 sin x 4- f cscx cot x dx 4 cos x 5- S 3+…

A:

Q: 2. y= 4sin(2x- T) and y= cos(3x-) 2

A: According to question given that y=4sin2x-πy=cos3x-π2

Q: 2. Locate the first positive root of f(x) = sinx + cos(1 +x³)- 1 where x is in radians. Use four…

A: (a) We need to find the root between 1 and 3

Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

A:

Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: Find L{(t- 2) (3 cos 5t + 1)}. COS 3(s2-25) (s²+25)? 30 | s2 s2 +25 6. 3 g3 s2 s2 +25 s(s² +25) 6s…

A: Find the Laplace transform of  L{(t-2)(3cos5t+1)}

Q: Evaluate f cos 2x dx sin8 2x O A) -csc 2x/14 + csc 2x/5 - csc 2x/6 + C CSC O B) I DONT KNOW O C)…

A: Explanation of the answer is as follows

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

A:

Q: 7. Find the first 2 iterations for the root of f(x) = x- cosx by the Secant method on [0,1.

A:

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

A:

Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Q: find the roots of the equation x*cos(x) = -1 In[-2,4] using bisection method with error = or less…

A: For the solution of the problem follow the next step.

Q: If we let u = 4x – 1 for theS 2 tan(4x-1)-3 cos² (4x-1) dx, what will be the resulting integrand?…

A: Solving the problem by finding the integrand.

Q: 4x – 1 for the 2 tan(4x-1)-3 cos² (4x-1) dr. what will be the resulting integrand? If we let u =…

A:

Q: find all solution of z   sinh(2z)=-1

A: Consider the provided equation, sinh2z=-1 Find all solution of z. Apply the trigonometric…