Pls kindly help to solve the below equationm to find w(x) =? P(x) = x + a² S (v – x)p(v)dv Hint: the correct answer is p(x) = Asin(ax) + Bcos(ax) then ф(x) sin(ax) a

Q: - ) s2 – 4 2s+6 What is L -2 cos 2t-3 sin 2t A.

A: find the inverse laplace transform of L-1-2s+6s2-4 we can write the function as…

Q: 2. Eliminate the arbitrary constants of the equation below, where B is a parameter. x = c1eßt + c2…

A: Given, x=c1eβt+c2e-2βtSin 2t-4t3 To eliminate the arbitrary constants of the above equation.

Q: 2:)y= 2x cos G) yous? (x²) +y sin² (x?) 2

A:

Q: Find Duf at P. 3 f (x, y) = sin(3x – 5y); P(5,3); - - NOTE: Enter the exact answer. Duf =

A:

Q: try also solve this by Variation of Parameters method! Solve the following initial value problem: y"…

A:

Q: A. Obtained the general solution. 5.: 6. (D² + 1)y = cos x

A:

Q: x³Væ² + 1 dx

A: Solve the integration

Q: dy Solve x da + 5y = x sin (ax2)

A:

Q: Q Is the equation e + x cos x 2 = 0 has real roots?. -

A: To show there are real roots, just use intermediate value theorem on appropriate interval.

Q: Q4) Choose correct answer: 1 csin-(cosx) dy dx = 1-п а. 1-n b. -2 1+n С. 2 1+n d. -2

A: The given expression is ∫01∫0sin-1cosxdydx.

Q: Q3\ find General solution of sin (xy). (ydx + xdy) = 0 %3D

A:

Q: In x2/25+ x² dx , we let x= 5sine. T True F False

A:

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

A:

Q: try also solve this by Variation of Parameters method! Solve the following initial value problem: y"…

A:

Q: Q3/B/By using Newton-Raphson method, then the value of the root of the equation x = cos (2x) when x,…

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

Q: using undetermined coefficients (D^2-2D+2)y=24e^x sin3x

A: Given: (D2  -2D+2)y=24ex sin3x

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d²y dx2 dy + 9x? + 6х— — бу %3 1+x3 dx

A:

Q: C. y = e2x sin²(3x)

A: We use product rule to find derivative for part c

Q: 3. L sinh %3D 4s .a O 4s²-9 3s .b O 3s2 - 4 12 .c O 16s?-9 9s 9s2-16

A:

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: 2x Show that y = e²* sin 3x satisfies the equation y"-4y'+13y=0.

A:

Q: he • (D'+D)y(x) =x The general solution to the equation y(x) =-G cos(x)+c, sin(x)-x* + 3x² +q 4 y(x)…

A: find complementary and particular solution to find the general solution.

Q: 3 dy Зу =-sin -1 2 - sin +C V4-9y2 3 A) True B) False

A:

Q: f (x) = xe-* – sin?x Newton Raphson (1st Method) @ x1 = 0.5 Newton Raphson (2nd Method)@ x1 = 0.5…

A: Newton Raphson Method:- Hence by Newton Raphson Method Root of the equation is 0.61447 (correct…

Q: For the equation y" + 4y = 0, (a) Show that y(x) = A sin wx + B cos wx is a solution for all values…

A:

Q: (a) S(7 – sin(x) + 9cos(x))dx - 1 (b) S (e* + 3* – - 2 V1-x

A:

Q: solve for y'. y=sin-1[(ax+b)/(bx+a)]

A: Sin-1x can be written as asin(X)   So we have expression as y=sin-1(ax+b)(bx+a) We have to solve for…

Q: Q3/B/By using Newton-Raphson method, then the value of the root of the equation x = cos (2x) when x,…

A:

Q: Determine the form of a particular solution y, (x) for y" - 4y'+5y e*+xsin 3x- cos 3x. [Do not…

A: Solution: The given differential equation is y''-4y'+5y=e5x+x sin3x-cos3x. For the complimentary…

Q: Scos(ex).cos"x dx

A: ∫cos3x.cos2x dx=∫cos(5x)+ 3(cos(3x) + cos(x)) +cosx8dx= 18∫cos5x dx + 38∫cos3x dx + 12∫cosx dx=…

Q: Find the general solution: 2y" + 3y' +y = 2e2 + x² + 3 sin(x).

A:

Q: d²y + y = 4 cos x dx² Please solve this equation by hypothesis (V)

A:

Q: A particular solution of y" + y =sinx + xcosx a. x?sinx - 2xcosx) 4 b. (x?sinx – xcosx) 4 c. (x?sinx…

A:

Q: Find L-s+9)2–36 e- 76- –9t sinh6t 16 e-cosh6t 6. 16 e "cos6t 16 9t

A:

Q: Show clear work on your paper. Is y = t + 1 a solution to y' =1+t² – 2ty + y² ? с — t O yes O no O…

A: Given: The differential equation y'=1+t2-2ty+y2.

Q: Example: Find the general solution of the equation a²z = e2x+3y + sin(x- 2y), H.W. +2 дхду

A: Given partial differential equation is ∂2z∂x2−3∂2z∂x∂y+2∂2z∂y2=e2x+3y+sinx−2y......1. We have to…

Q: :Q1) Solve the following Vx = x². Ve2 3 Q2) Solve the following: e3 x3 = Q3) Solve for (y) if:…

A: Solve the following

Q: 1. S x+cos 2x dx x2+sin 2x 2. Sxe**(ex² + 1)'dx

A: According to the definition of definite integrals, if dFdx=f(x), then ∫f(x)dx=F(x). In this problem,…

Q: y" - 4y' = t + 3 cos (t)te %3D

A: Given The given differential equation is y'''-4y'=t+3cost+e-2t.

Q: 2. Obtain the general solution using Bernoulli's equation. Simplify your final answer. 3 (2y° + x/…

A:

Q: dv Solve ax + by + c dx

A:

Q: 3. L [f(3)] if f(t) = e-³++³ sin3t

A: Given ft=e-3tt3sin3t

Q: 4) B: Solve for x: az + vx-4 + y sin2x) < 4cos2a laxdy

A: Given - ∂2∂x∂y y3+x-4 + y sin2x &lt;4cos2π To find - the value of 'x'

Q: 2 S tan x sec x dx e-0.3x =27 Q5) (A) Evaluate (B) Solve for x: |3D

A:

Q: Test for exactness and find the general solution. (2xy – sin x) dx + x²dy = 0

A:

Q: 2 Show that y = sin(t) is a solution to ( dt =1– y. To do so, compute each side of the equation in…

A:

Q: | 8(x + 1) (2x2 + 4x – 1) dx 3/2 5.

A: For the given integral- I=∫8x+12x2+4x-132dx Let u=2x2+4x-1 Differentiating w.r.t. x to both sides-…