QUESTION 17 (x() If X= x2(t) is solution of the IVP X =0 1 (0 4 -4) X(0) =0 then x1(t)+x2(t) +x3(t) = 00 1 Oa -3e'+1 Ob-Se' +1 Oc Se' +4 Oa-3e' Oe -3e' +4

Q: (2x+1) (x+1) y"+2xy' - 2y = (2x+1)- A solution of the homogereous Jorm is → y= (x+1)-1 Find the…

A: The differential equation is provided below, 2x+1x+1y''+2xy'-2y=2x+12 And one of its solution is…

Q: 6. What is the general solution of * (x2 + 2xy – 4 y)dx – (x? – 8xy – 4y²)dy= 0 x2 – 4y? = c(x – y)…

A:

Q: c. y' + 2y = x³ with y(1) = 2 Yo (x) = e Yp (x) = y (x) = y (x) = -2x 1½ e ²x³ - 2/ ( 10²x² -…

A:

Q: Find the explicit solution of dy/dx=2xy² + 3x²y², y ( 1) = − 1 O 1/y=3-x²-x3 Oy=x²/2+x²³/3-3…

A:

Q: ,(x) = (x-x+1) y'(x)+3y'(x)+9 y(x) = 5x' +1 true false

A: False

Q: 1 -3 1. 10. The general solution of x' = -1 1 -1 |х is 3 -3 -1 3 (a) x = Ce-t -2 + C2e*| 3+ C3e* | 1…

A:

Q: The differential operator (D+4)3 is supposed to annihilate the function z2e-4, we will check that:…

A: To check how the differential operator D+43 is supposed to annihilate the function x2e-4x.

Q: 1 2 9. A fundamental set of solutions of x': -3 -1 3 x is: 3 2 -2

A: We are entitled to solve only one question, so we will answer only the first question. Please post…

Q: Solve the DE: dy + 2xy = 2x³y3. dx

A: The given problem is to solve the given differential equation. The given differential equation is of…

Q: .1) The general solution of the equation y" + y =-5e- , is: - y(x) = Ce-* + ez(Acosx + Bsinx) -e-* O…

A:

Q: If x=√√ 1-t and y=-3t+1³, what is y'? (Α B (C) D -6 (t-1) (t+1) √√1-t 6(1²-1) √√1-1 -3 (1²-1) √√1-1…

A: x=1-ty=-3t+t3y'=dydx=dydtdxdtdtndt=ntn-1

Q: 1. If y = In(V x² +1 ) , then y' = 2x (b): 2x (a) x² +1 3(x2 +1) () 3(x2 +1)-2/3 (d) 3(x2 +1)

A: y=lnx2+13⇒y=lnx2+113⇒y=13·lnx2+1   ∵lnxy=ylnx

Q: 10. A fundamental set of solutions of x' = 3

A: Given,        x'=-21-13-343-12x

Q: y(4)-y'''+2y''-2y'+4=0 1 is a solution of the characteristic equation. Find the general solution to…

A: According to the given information it is required to calculate the general solution of the equation:

Q: The general solution for x' = + 3 1 a) x(t) = G e-21 + C₂ (₁¹) e b) x (1) = a (1¹) e (1¹) ₁²¹ + ₂(1)…

A:

Q: Which of the following is a general solution to the following: x²y" + xy' + (36x² − 1) y = 0 A. y =…

A: Solution:

Q: 1 -1 4 x is: -2 10. A fundamental set of solutions of x' = 3 -3 3 -1 () (a) x1 = et 1 X2 = e-2t 1…

A:

Q: 20. In question number 19, what is its particular solution? " (D² – D - 2)y = 1– 2a – 9e- Yp = 3e- +…

A: We need to find the particular solution of D2-D-2y=1-2x-9e-x Now, the particular solution is:…

Q: The differential equation y' = Vx+y+1–1 has the solution:

A: We need to solve the differential equation given by y'=x+y+1-1 The solution is given below.

Q: 14. The general solution of y' - 4y = 2e²√√y is:

A:

Q: Find the general solution to the following problems a) x²y" - xy' + y = x² + 1.

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

Q: A fundamental set of solutions of x' = 3 2 x is: 1 (w) x. - “(;). x-() (F). (1). *--(;) (a) x1 = et…

A:

Q: y(k +2) - y(k + 1) + 2y(k) = 2* with y(1) = y(0) = 0 %3D

A:

Q: Find the general solution of (1) yV – 2y" + y" = 24x² + 12x +8

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

Q: 1 9. A fundamental set of solutions of x' = | -3 -1 3 x is: 3 2 -2 2 (a) x1 = e-2#| -3 , x2 = e-t X3…

A:

Q: What is the particular solution of y'=x²-2x+3,ify=4whenx=0? (A) B y=x²-x²+3x+4 3y=x²-3x²+9x+12…

A:

Q: 0 1 0 0 0 1 x is: -12 8 1 5. The general solution of x' = 1 (a) x = C,e-3t -3 |+Czeª | 2 |+ C3e-2t…

A: The given system is                                         x'=010001-1281x To find the general…

Q: 6. {y₁(x) = x, y₂(x) = x²} is a fundamental set of solutions of the reduced equation of x²y" - 2xy +…

A: Given that y1x=x , y2x=x2 is a fundemental set of solutions of the reduced equation of…

Q: Find the particular solution : y" – 2y' - 3y = 2e-t +3 (a) Yp =e-t +3 (b) Yp = -te-t 1 =-tet -1 (d)…

A: Particular solution

Q: 5. y = gezt + cze-3t – cost o y" - 7y' +y = sint + cost o y" +y' – 6y = 5 sint – cost o y" +y' +y =…

A: Find y , y' and y'' and substitute in the given option and check which option is true. Note : As per…

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: 3 5 1 -1 a) x(1) = q (₁²¹) e² a (1¹) e ² + c₂ (₁) ₁² b) x(t)=q| 11) e ²² + 0₂ (1) ₁1e ²1 c) x(1) = q…

A: We have to find the general solution.

Q: -6 -4 9. The general solution of x' = x is: (w) x - Ce () + C [(-4) +(-)] (3) * = Cye" (:) + C" (…

A: