3 4. If y = t3 + 3t? and x = t - 8t2, show that y" = 16t(t+2)(t-2)3

Q: 2. Eliminate the arbitrary constant on the given equation: y = C₁e-²x + De4x

A: Given  y=C1e-2x+De4x

Q: 9. Solve d²x dt² + 4x + 5y = 1²; d²y dt² + 5x + 4y = t +1.

A:

Q: 11. Find the particular solution of 2ydx = 3xdy, when x -2, y = 1

A: Given : Differential equation :  2ydx = 3xdy And x = -2, y = 1   To find : Particular solution of…

Q: 3. Find the general solution for y" – 10y' + 25y = 0 s.t y(0) = 1, y(1) = 0

A:

Q: 4. xydx + (y √ x² + y²-x²) dy=0

A:

Q: Q.1 Solve the IVP: y" + 3y' + 2y = 686(t) with conditions: y(0) = 0, y'(0) = -1.

A: The given initial value problem given is y"+3y'+2y=6δ6t       with conditions y0=0, y'0=-1…

Q: 3. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solution of y" + 4y = 0?…

A: Given, y''+4y=0 a second order differential equation. To show that y(x) = C1 sin 2x + C2 cos 2x is a…

Q: 1.Solve the given problem W = f(x, y, z) = 3x²y+ yz² + 2z³ fxis equal to ? fyis equal to ? fzis…

A: Follow next step

Q: x'y" – 3xy' +4y=x° Inx

A:

Q: A)y= 3xt4 and -15x t Sy=2 Infinety mony Solutions B)y=-2x tl and Zx ty=1 One so lution ()y=2x-4and…

A: topic - linear equations

Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

A:

Q: 41n <ys 28 31r x = sec* (7t) – 1dt, | 21 41x 28

A:

Q: What is the general solution of xydx−(x2+3y2)dy=0

A: Topic :- Differential equation

Q: Find the solution (varition of parameter)   X2y11-2xy1+2y=x3sin x

A: According to the given information, it is required to find the solution of the given differential…

Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

A:

Q: y" -4y' + 13y :

A:

Q: m21 is nine times as large as m z2. Find mz1. -1 is supplementary to 2.

A: m∠1=9  m∠2                                       ------(1) and  m∠1+ m∠2=180°…

Q: (b) If z = 9t²e 4, find dz dt 4

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 7. Eliminate a and b from the equation y =- In(ar +bx) where a,beR-(0}

A: q-7 eliminate a and b from the equation y=12lnax2+bx  this can be written as 2y=lnax2+bx⇒e2y=ax2+bx…

Q: Use variation of parameters to find a particular solution of 14aie" 3 y" – 2y' + y - Yp(x)

A:

Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: SOWE FOR THE ORTHO GON AL TRAJECTORIES y² = 4x² (1-ex)

A:

Q: Find the general solution to the DE using the method of Variation of Parameters 8 y" – 4y = e2x + 1

A:

Q: Find the Solution (1+r)ds + 2sr-3(1+r)dt = 0; when t - 0, s = 2. ® : (1 - P12-e* ®= (1 - s12-e © : =…

A:

Q: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Find the general solution of y" – y' – 2y = cosh 2t.

A:

Q: dy 3. Solve dx = -8xy² +4x(4x+1)y-(8x' +4x² -1) by knowing u = x is a solution.

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

A:

Q: ind the particular solution of (9x-2yldx- x(6x- yldy-0 when x-1. y=1 To start let y-vx

A:

Q: V Solve usinog variaton of parameters or reduction of order (D²- 2D+1) y = e2"(e*+1)?

A: Solve by using variation of parameter  find auxiliary equation and then find wronskian and put in…

Q: Show that y = - In x + 3x - 5 is a solution of y" -=0. Use y = - Inx+3x – 5 to find y' and y". y' =O

A:

Q: 3X 7- (0²1)y=K²" yp-e (4X-3} 8-(0-20+4)y=x+3x-5x+2 yp=Dx yo= 3.2 -2K 2. to-(D²+2}y=x²+xre+cos3X éte…

A:

Q: : Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

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

Q: Use the method of variation of parameters to solve the initial value problem x'=Ax+ f(t), x(a) = x₂…

A: We have to find the solution x(t) using the method of variation of parameters.

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: 5- Find the particular solution for: 2e2x – y = xy', x = 1 when y = 6 %3D

A:

Q: 4. Solve the equation T2T satisfying the conditions: at ax (i) T=0 when x= 0 and 1 for all t 2x,…

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

Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

A:

Q: (4) B/ If Ø = (x³y²z) and A = 2xz 1-3y2j+ 3xy²k Find ?у ?х the point (2, -1, 3)? at

A: Given:        ϕ=x3y2z         A=2xzi^-3y2j^+3xy2k^         ϕA=x3y2z2xzi^-3y2j^+3xy2k^…

Q: 10. Solve: (2st +1 kds – 3s° dt = 0, s(-1)=1 a. 8st' = (s -t) – t)² c. 8st = (t – s) 3 а. 8st3 b.…

A:

Q: 5. Use variation of parameters method to solve а. a. y" – 2y' + y = 1+x2

A:

Q: 2 Verify that for r > 0, y = r is a solution to yy = x. V3

A: Double differentiate to prove the given

Q: 8. Obtain the particular Solution by satisfying the conditions indicated. y' = x exp (y - x²); when…

A:

Q: 2. Obtain the particular solution. y"-y'-6y=0; when x=0, y=2,y'=1

A:

Q: (b) Find the general solution of: = yx² - xy ax Given z = y when x=1, determine the particular…

A:

Q: 1 Solve 1 3D7 for z. y. 1-

A: 1x-1y-1z=7

Q: f(x) = 2x5 + 15x4 - 3x3-4x2+ 7x+ 14 1)Trapeaoidal rule 2) Trape20idal rule with n=2 3) 1/3 Simpson…

A:

Q: Show that xy – 2 = cxy is a solution of (x² + y2 – x)dx – ydy = 0.

A: Given  x2+y2-xdx-ydy=0 dydx=x2+y2-xy