12 d3x(t) 5 dt3 d²x(t) dt2 + 5x(t) = 3cos(2t) d²x(0) = 2, dx(0) 1, x(0) = 1 dt2 dt

Q: Higher Order Linear Differential Eqation (D2-2D+10)2y=0

A: We will solve the problem

Q: dx 8х — 9у dt dy = x + 2y x(0) = 2 y(0) = 1 - dt

A: The solution is given as

Q: 2 y

A: According our guidelines i solve only first question.For second solution please resubmit again…

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t x(t) general solution function

A: Given equations are                                              dxdt+dydt+x=e-t           ...…

Q: 5 0 2x +2 dy dx dz in the order dz dx dy 0 -1 0 5 0 2x+2 0 -1 0

A: Given that ∫05∫-10∫02x+2dydxdz The objective is to show that, ∫∫∫dzdxdy In the interval,…

Q: d²x dx 2 + 10x = e2t x(0) = 0, x'(0) = 1 %3D - dt2 dt

A: Given differential equation is d2xdt2−2dxdt+10x=e2t. and x0=0, x'0=1 Write the auxiliary equation…

Q: Determine whether the equilibrium at x = 0 is stable, unstable, or semi-stable. dx 4x² - x³ dt 3 The…

A: We need to find the equilibrium at x=0 is stable, unstable, or semi stable. given,…

Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: dx for 4xy - 5x + 2y3 = - 42, with the conditions dt = - 6, x=2, y= - 2. dt Assume x and y are…

A:

Q: 1. S (5x-12) dx 2. S x³-6x² +8x 3. S -(3 cos² 0 +8 cose-12) sine de cos³ 0+7cos² 0+ 12 cos 0 dx…

A:

Q: S2x²e** ax=uv- Jvau -Svau. Sfoxe". Using Integration By Parts, Find uv- Jv du- 3 x² e dx O 2 x3 x3…

A:

Q: 3 - y cos xy - 4x ) dx + (- 2x+3y x cos xy + 2y) dy = 0 - | 2x+3y 2.

A: Compare the given equation with Mdx+Ndy=0 to obtain M and N. Calculate the partial derivatives of M…

Q: QI Find d for dt dy = 4e - 5x'e0 dx dy 3x e +5x'e dx الخبار ه 2 dy dy 2xe 2e + 4xe* dx dx dy 5x'ere…

A:

Q: 12 d*x(t) 5 dt3 d²x(t) dt² + 5x(t) = 3cos(2t) d²x(0) 2, dt2 dx(0) 1, dt x(0) = 1 3s2 + 5s + 1 X(s) :…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: D. Fina the total differential of the function xye¬(x²+y*),

A: Given: f(x,y)=xye-x2+y2

Q: y=(1+2cot"x) 3 dy_ 8(1-2cot"x) dy 8(1+2cotx)° %3D dx 1-x dx 1+x? Op tion 3 Op tion 1 dy -8(1–2cot"…

A: Let's find.

Q: Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

A:

Q: 5. dt3 d³x(t) 8 d²x(t) dx(t) - - dt + x(t) = u(t) 14 dt2 d²x(0) 1, dx(0) x(0) = 1 -2, dt2 dt

A: Given below the detailed solution

Q: QI Find for dx dt dy 4e - 5x'e dx dy 3re + 5x'e" dx O 2, dy - 2e + 4xe dx dy 2xe dx dy dy 5x'er dx…

A: We have to compute dydx, where y=∫x6x5et2dt. Comparing the given integral with the equation…

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t     x(t) general function solutions

A: This system has been solved by the elimination method, by eliminating y to get the general solution…

Q: d²x dx (v) - 2 + 10x = e2t x(0) = 0, x' (0) = 1 dt2 dt

A:

Q: dx dy - x – 2y = 16te', 2x - dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: The given differential equations are                                  dxdt-x-2y=16tet ..............…

Q: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

Q: A _1. (2x – 3) dx A. -2 _2. L(x3 + 2x) dx В. 0 _3. (x² – 2) dx 1 С. 3 4. S(x3 + 3x – 1) dx 2 D. 2 |…

A:

Q: x +1 -dx x² (x – 1) (a) Integrate

A:

Q: 2 Solue Bor メ= o-5 dx = y X (6) = 0 dt dy =_X yo) =I %3D

A: As per bartebly Guideline we can solve only one question.. Hope you understand

Q: Find dy/dt.

A: Find dydt.

Q: 1/4 sec2(t) dt J-x/4

A: Given: I=∫-π4π4sec2tdt

Q: dy 2. if y = In(x² + 1) Then at x=1 %3D dx 2- 2 In 2 2- 1 1- 4- 1/2

A:

Q: d²x 2. dt dx dx 2- + 3x = 0 x(0) = 1, (0) = 0 - dt2 dt

A:

Q: dx + 2– + x = u(1) x(0) = x'(0) = 1 dt

A:

Q: In x -dx C. d. 5% dx хе fx(2x +1)* dx е. f. In(x + 1)dx x2 dx Vx + 2 g. x4 h. dx Vx5 + 1 4 i. j. 1…

A: From the given problem:   c).   I=∫lnxxdx..1     Let,   lnx=uddxlnx=dudx1x=dudxdx=du Substitute…

Q: b) y = [ dx Integrate. 13 +5

A:

Q: Aparticle moves on the graph of y^2=x+1 so that dx/dt=4x+4 what is dy/dt whrn x=8?

A:

Q: dy for 2xy - 4x +2y3 = - 32, with the conditions dt dx 3 - 4, х%3D2, у%3 -2. Assume x and y are…

A: 2xy-4x+2y3=-32 Differentiating with respect to t, we get…

Q: 2. Evaluate the integral. -2 (a) (x² – 3x) dx - -1 •3 (b) Lce L(e + 2)(t – 3) dt -2 (c) 2.9 x° dx

A:

Q: d²x dx dx -(1) = 2 4- + 4x = 0 x(1) = 0, - dt2 dt

A:

Q: x-2-x-4 The differential of y=- -2 - x -3 A dy =d xp - B dy= - -dx dy =-dx D dy: -dx is

A: we have to find

Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

A:

Q: 2x lerivatives from first principle, find the derivatives of y = 5 V3x-e2x-(xln x)(In(In x)) -2e2x)…

A: We have to find the derivative from the given function

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: d²y + 6(x² + x) sin x dx² d²y + sin x dx2 dy dy + 6y sin x – 6 sin x dx dy = sin x + x²sin³x +…

A: In this problem we first simplify the equation to get Cauchy-Euler form and then solved the…

Q: dx = -18, x 6, y= -3. for 3xy 7x+6y3 = -258, with the conditions Assume x and y are functions of t.…

A: given:

Q: d²x dx + 4- + 5x – 10 = 0, when t = 0, x = 0,x = 0 dt2 dt

A:

Q: - = 2x, – x, dt dx, =-x, +x, +4e' dt

A: integrating, x1= (x1)^2-dx2/dt, replace dx2/dt with -x1+x2+4e^t in above equation…

Q: d²x + 16x = 1 + 2 sin 4t dt2 dx (0) = 0 x(0) = 0, %3D dt

A:

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A:

Q: d2x/dt2 + 4 dx/dt + 3x = 2 x(0) = x’(0) = 0

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

Q: (ii) + 6x dt cost, x(0) = 0.1, x'(0) = 0 %3D %3D dt2

A: (Note: We are entitled to solve only one question at a time.) Given: d2xdt2+5dxdt+6x=cost, x0=0.1,…