Find x E R that satisfies -2 , – 02 + 2 vz U2 det = x det + – ö4 2 0 + 03 U3

Q: Solve the D. E. to the I. V.P. (1 +x² + y² + x?y²)y' = y², 2. y(1) = 1

A: The solution is given as

Q: IV. Solve for x using the fact that if a" = a", then v = w. (Show solution) 6) 5x-1 = 0.042x %3D 7)…

A: Use the fact, "If av=aw, then v=w" to solve the following equations for x.

Q: The function y,(t)=2t+e is a particular solution to y"-3y'+2y=4t-6 Select one: False O True O False

A:

Q: For the equation Mdx+Ndy=0, if both M and N follows that f(Ax,\y)=^k f(x,y), the equation is A.…

A:

Q: Let us solve the following equation via separation of variables J²u(x, t) Ət² = 7 d²u(x, t) ?х2 a)…

A: The given equation is ∂2u(x,t)∂t2=7∂2u(x,t)∂x2. Solve the equation by using separation of variables.…

Q: C. Given :v = (3t - x)e-2 , 1. Find at

A:

Q: Find the Solution (1+12) ds + 2t[st² – 3(1+12) 2]dt = 0; when t = 0, s = 2. %3D

A:

Q: Let z=xln(x2+y²-e*)-154xy, x=te, y=est. If the value of Oz when s=2 and t=1 is equal to Ae?+Be, then…

A:

Q: Q2/ A/ Find the and ar * iff (x.y) = x - xy, x=r² +s and y =r-s as

A:

Q: Find the solution to ty' – y = r² e 0.09 ' satisfying y(1) = 0 and valid for all t> 0.

A:

Q: Using the indicated substitution, find a general solution in terms of Jy and Yv. x?y" + xy' + 36y =…

A:

Q: (c) If f (2) = (2³ + 6) e'0-, 10z and f' (6i) = re®̟ then what is the value of r² ?

A:

Q: Q2. If the solution of the below first order D.E is y = C ef(x,y) (x³ + xy²)y' = y3 Find the f(x,y).

A: x3+xy2y' = y3dydx=y3x3+xy2 ........................equation(1)Let put y = vx in equation(1) and…

Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' + y = 0. If W (y1, Y2)(2) = e² , then…

A:

Q: Let y(x) = c1 + c2x + C3 et is a general solution for D. y" + ay' + by +cy 0, Find the value of a?

A: To answer the given question, we form a differential equation from given general solution.

Q: Note that y(t) = c1 + c2t + (t^(3) /6) is a general solution for y''= t. Find c1 and c2 such that…

A: Given equation is y''=t The general solution of the equation is given by  yt=C1+C2t+t36...........i…

Q: Q2. If the solution of the below first order D.E is y = C ef(x.y) (x³ + xy²)y' = y3 Find the f(x,…

A:

Q: Q1.Find the general solution of following PDE equation (a) (5z+ R)uz + (7x+ R)u, R (b) (z + R)u, +…

A:

Q: a) Are Y1 and Y2 independent? b) Find V(Y1 – 2Y2), if we know that E(Y,) = E(Y 2) =}.

A:

Q: I. Obtain the general solution of the following: a) (D2 + 3D + 2)y = 1 + 3x + x2 b.) (D2 − 6D +…

A: Use rules of differential equations

Q: Q2. If the solution of the below first order D.E is y = C el(x.y) (x³ + xy²)y = y³ Find the f(x, y).

A:

Q: Let y1, Y2 be two independent solutions of t?y" – 2y' + (t + 3)y = 0. %3D If w(y1, y2)(2) = 3, then…

A:

Q: b) (i) Show that dz is a constant independent of z, and R. { Hint : z= Z, + Re"} 1 +- 2z-4 2 -z 3…

A:

Q: r In y dr, where D is described by 1 < r < 2, e <y<e aD | V1 +r² dy, where D is described by -1<r<1,…

A:

Q: Find values of m so that the function y = e"™x is a solution of the given D а) y' + 2y = 0 b) y" –…

A: Using differential equations ,

Q: #X-N, (M. E) where QX)-2X +3X;-2X,x, Find M.

A:

Q: (e) f(x1,x2) = xỉ/x2 on R x R++.

A: The solution of (e) is in below

Q: Q2. If the solution of the below first order D.E is y = C ef9) (+xy)y=y Find the f(x, y).

A:

Q: 2. For r(t) = (4t + 3)i+t²j+ (2t² + 4)k, (a) find r'(t), (b) find r"(t), (c) find r'(t) r"(t),

A:

Q: - 4. Find the D₂R(t)|| and ||D,R(t)|| if R(t) = 2(e² − 1)i + 2(e² + 1)j + e¹k.

A:

Q: 7. Find the general solution of the following DE. a. (D2 – D- 2)y = 0. b. (D2 + 3D)y = 0. c. (D? – D…

A:

Q: If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

A:

Q: (D² – 3D + 2)y = e2*(1+e2x)

A:

Q: Find CE R such that x(s) = 2 - Ce-s is a solution of the IVP x' = 2-x, x(0) = 3.

A: Introduction: Initial value issues are a specific kind of calculus issue. Calculus initial value…

Q: 9. Find the general Solution of the following DE. a. (D - 4D2+ 4D)y = 0. b. (9D + 6D² + D)y = 0. c.…

A:

Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

A:

Q: Find the general solution of the equation ¤(x – 1)y" – (2x – 1)y' + 2y = 0 by the reducing the…

A:

Q: Find the value of y, for wich the solution of the I.V.P y' - y =1+3sin t, y(0) = yo remains finite…

A: Here we are given an I.V.P                                         y'-y=1+3sint Also it is given…

Q: Q2. If the solution of the below first order D.E is y = C el(x.y) (x' + xy?)y' = y³ Find the f(x,…

A: Given that The solution of th given D.E. is  y=Ce^f(x,y)

Q: If y = f(x) is the solution of æy' + 13y – axy? = 0, f(1) = 12/a, where a + 0 is a re а, number,…

A:

Q: ux+ h) – v(x) , Given that (x) = 2x² – 5x +2 which of the following is equivalent to (A) 2h+4x - 5 B…

A: Basic functions problem

Q: (c) Find PMF of X and using that find E[X].² (d) Find P(Y > 5 | X = 3)

A: Joint distribution:PX,Y(x,y)=223614x-113y-1; 1≤x≤yMarginal PMF of…

Q: C. Find for the general solution of the following DE. 8. (D3 + 3D2 – 4D)y = 0 9. (DA + 6D3 + 9D²)y =…

A:

Q: Let us solve the following equation via separation of variables 8²u(x, t) Ət² 8²u(x, t) dx² a) After…

A:

Q: If y = 2x-5, x is a r.v., then E(y) can be calculated by M', (t = 0)=(e-st M, (2t)) when t = 0. O…

A:

Q: Find dy for the given values of x and Ax. y = /2x+9; x=1; Ax= 0.12

A:

Q: Obtain the particular solution of (3x² – 2y²)y' = 2xy when x = 0,y = 1. a. x2 = 2y² (y + 1) c. x2 =…

A: Let's find.

Q: Solve the second-order DE y"+2y'+4y= g(1), y(0)= 0, y'(0)=1, where 2, Ost<2 g(1) ={-2, 2si<4 0, 124.

A:

Q: Q2. If the solution of the below first order D.E is y = C ef(xy) (x³ + xy2)y' y3 Find the f(x,y).

A: