2y – x = 3t y + x' = 3e-t ¤ (0) = y (0) = 0 3(s-1) L (x) s2(s+1)(2s²+1) 3(2s-s-1) s2 (s+1)(2s²+1) L (x) = L (x) = (3s+1) s2 (s–2)(2s+1) 3s2 L (x) = (s+1)(s-2)(s²+1)

Q: 4. For y' = y3 +y² – 6y, Find the critical points. Draw a phase diagram and mark the critical points…

A: Given y'=y3+y2-6y Given a differential equation y'=fy a point y0 is said to be a critical point if…

Q: 1) Use reduction of order method with y₁ (x) = e-2x to find a second solution y2 for the DE: y" - 4y…

A: Solution :-

Q: 4. Find the general solution of (x + xy²)dx + ye²² dy = 0. O ln(y² + 1) — 4e¯x² = C O e ² + 2ln(y² +…

A: Given is the differential equation (x+xy2)dx+yex2dy=0 The objective is to find its general solution.…

Q: 2x4 +3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x) B + x-5 C E dx (x +…

A:

Q: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

A:

Q: Find the solution of the given initial value problem. y(4) 4y" + 4y" = 0; y(1) = 11+ e², y'(1) =…

A: The given problem is 4 order homogeneous linear differential equation. First we find the auxiliary…

Q: Problem 2.3 i. and 2.3 ii

A: Given initial problems are

Q: d²z 2+ 3-2z = te-2t ; z(0) = 0 z'(0) = -2 dt2

A:

Q: (- 1)"x" .n (– 1)"x2n (2n)! (– 1)"x 2n+1 V3 = = n=0 (2n + 1)! n =0 n! n = 0 is asolution for D.E

A: Note that, ∑n=0∞(-1)nxnn!=e-x∑n=0∞(-1)nx2n(2n)!=Cosx∑n=0∞(-1)nx2n+1(2n+1)!=Sinx

Q: 9 Consider the initial value problem y' – y = 7t + 2e', y(0) = yo- Find the value of yo that…

A:

Q: (x-2)²(x³-4) y = Vx2+1 dy If then equals to : dx O y [2/(x-2)+(3x^2)/(x^3-4)-2x/(3x^2+3)] O…

A: The formulas which are used to solve the above problem are stated with the solution.

Q: Solve the initial value problem. nt 5y' – 2y = e-7, y(0) = a Let ao be the value of a for which the…

A: We will find integrating factor of equation.

Q: Find the general solution of (xy + 4x)y = 5y² + 4xy². a) Oy + 12y- = -5 In |x| – 16x + C b) Oy - 4y-…

A: First order non linear ordinary differential equation.

Q: Q1.O Determuine type and stablity of critical point. y = 24, t4z 2

A:

Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

A:

Q: 47x +75y -30x - 48y satisfying the initial conditions r(0) = 19 and ly' y(0) 12. x(t) = y(t) =

A: Given equations  are  x'=47x+75yy'=-30x-48y  with the initial conditions x0=19 and y0=-12 To find…

Q: 3 (D2 + 4)y =- Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} °L{y} = 1 3. 3e 3s Se-3s 82+4 s(s2+4) s (s²…

A:

Q: 4. Solve the initial-value problem dr = -2r - 2y dt dy -2r + y. dt where the initial condition is…

A:

Q: 5. The function h(x) = x² + bx² + d has a critical point at (4, -20). Determine the constants b and…

A: This question is related to the application of derivatives.

Q: (D2 – 1)y = 2 2t -4 0st<2 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) 4 2e -2s 6e-2s s2 (s² –1) s(s2 -1)…

A:

Q: (1) L{y"-3y'+2y} = L{4e²"} 4 (2)[s*F(s)– sy(0)– y'(0) – 3[sF(s)– y'(0)]+2F(s)= -2 4…

A:

Q: (2t - 4 0st<2 (D2 – 1)y =- 12 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) = F1) 4 2e-2s 2e-2s %3D -…

A:

Q: F(s) = exp(-s) exp(s) -exp(s)/s² 2/s³-1/s² -exp(s) (1/s² - 1/s) exp(-s)/s² 1/s² - 1/s exp(-s) (1/s²…

A:

Q: 1. y" - 2y' - 3y = e* by D- operator method

A: Since you have posted multiple questions so according to our guidelines we will solve only first…

Q: 19. Find the particular solution to y' = 2sin(x) given the general solution is y = C-2cos(x) and the…

A:

Q: 2. What is the solution to the initial-value problem PD.E. ut = c²uxx (u(x,0) = 0 lu,(x,0) = xe-x -…

A: Given that  utt=c2uxx    -∞&lt;x&lt;∞,  0&lt;t&lt;∞ux,0=0  and  utx,0=xe-x2,   -∞≤x&lt;∞ It is a…

Q: Verify the function y = xe^-x + 2 is a solution of the initial value problem: dy/dt = (1-x)e^-x when…

A:

Q: 5y" – 10y' + 1y = 30sin(3t) with initial conditions y(0) = 1 and y'(0) = 5 Be sure to clearly define…

A: The given second order linear differential equation is 5y'' - 10y' +y = 30 sin(3t) with initial…

Q: Solve dy 4y dx x(y - 3) By using the method of separable variables. 1- y - 3 Iny = 4 ln x + C Option…

A:

Q: y" – 2y – 2y = 0

A: Given:      y''-2y'-2y=0       -2yx-2ddxyx+d2dx2yx=0 The differential equation has the form:…

Q: 1.)(x + y - 1) * d * x - (x + 4y + 2) dy = 0

A:

Q: 1. Apply Taylor's method of order two with N = 4 to the initial-value problem y' = 4 + 1, 1<t< 2 y…

A: The Taylor series of order 2 for a function f(x) is given by f(x0+h)≈f(x0)+hf'(x0)+h22f''(x0) For…

Q: 2 Discuss the stability of equilibrium points of the following ODE: { (2 = -r³ + y°, y = -x.

A:

Q: III 1. dt2 fip +6- dt and the gen +8y=2e-3t am to nor 2. d'y dt2 fip +4 +13y=et dt 3. +10y = e

A: The objective is to find the general solution of the given differential equation.

Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy + 2xy = f(x),…

A:

Q: 4. (a) Compute the general solution for: +4- +3y=e-¹/2 dt² dt (b) Compute the solution with y(0) =…

A:

Q: (1, 0 2 L (2) = + e (-!) te-2s (s-1) S (음 + 1) O. e2 L (y) = -2s e - s2 ( (s-1) °L (y) = -2s e (s+1)…

A:

Q: 15 Consider the initial value problem y' - - y = 5t + 4e¹, y(0) = yo. 2 Find the value of yo that…

A:

Q: 2t-4 0st<2 (D2 - 1)y = t22 y(0)=0, y'(0)=1 Find L{y} L (1) = 1 + - - 2+ 4 2e 2s 2e-2s %3D | L (y) =…

A:

Q: -value problem y" + x²y' - 4xy = 2x³ +6x²-2, y(0) = 0, y(1) = ng method. Use the modified Euler…

A: Given as, The boundary value problem, y"+x2y'-4xy=2x3+6x2-2,            1       y0=0, and y1=2. By…

Q: 2,2 2 (xy +x)dx = (x'y+x+y+1)dy O In(x² – 1) =y² – 2y + 4ln|c(y +1)| In(x² +1) =y² - 2y +…

A:

Q: cln 4 cln 3 cln 2 10. Compute e0.5x+y-z dz dy dx.

A: Evaluate the integral: ∫0ln4∫0ln 3∫0ln 2e0.5x+y-zdzdydx=∫0ln4∫0ln 3ey+0.5x∫0ln2e-zdzdydx=∫0ln4∫0ln…

Q: 1. y" - y' - 2y = e by D- | operator method 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x)

A:

Q: Find the solution of ODE using the method of separation of variables. Initial value problem:…

A:

Q: Solve for the Y(s) of a given function that is in terms of y(t) with the corresponding initial value…

A: We have to find the Y(S) of given function

Q: Consider the initial value problem {y′−3y=6, {y(0)=1. What is the limit of y(x) as x approaches −∞?

A:

Q: Chapter Four d'y df² and y'(0) = 3. 2. 9. dy 24 +16y=0, dt given y(0) = 3 y =(3-1) e3

A: We have to find the solution of given differential equation.

Q: 1. E(Y,X, X2... X) (Y+Y2 +. + Yn) 2. E(IX,, X2, X) =E Y2+ + Yp) + -B(X, +X +

A: We have to show that β¯ is conditionally distributed.  To show β¯ conditionally distributed we will…

Q: Solve the initial value problem. 9y/ – 2y = e, y(0) = Let ao be the value of a for which the…

A: