Section 2.1 Exercises 1. Consider the following direction field for the differential equation = x2 - y2. Sketch, dx by hand an approximate solution curve that passes through each of the indicated points. Use different colors for each! а. у(-2) %3D 1 b. y(3) = 0 с. у(0) %3D 0 %3D

Q: 7) Determine the particular solution to the differential equation y 3x-2 that passes through the…

A:

Q: y(s) =. (s+2)² +1 e" (cost – 2 sin t) -2t e" (cos t – 2 sin t) O A.) O B.)

A:

Q: The Bernoulli equation y'+37 xy'= 34 y can be converted to one of the following linear equations: a.…

A:

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: We first obtain Dy, D2y, D3y, D4y, D5y for given particular solution y. Then we find which of the…

Q: Solve Ихх + t³× u(x, 0) = 0

A: solve the system of ordinary differential equations:dx/ds = 1dt/ ds = 1dU/ds = Ut + t2x from first 2…

Q: [2] Determine homogeneous the roots of the auxiliary equation y=x²-ecosx for a linear equation with…

A:

Q: Verify that the implicit equation x^2 − y^2 = C, where C is a constant,represents a solution to the…

A: To verify that the implicit equation x2−y2=C, where C is a constant, is a solution to the ordinary…

Q: a) x2y"+ xy' +(x2- 25)y = 0 b) (1 - x2) y" - 2xy' + 42y = 0 %3D %3D

A: a. Bessel ordinary differential equation has the form of x2y''+xy'+x2-v2y=0. Now, Rewriting the…

Q: Solve for a linear equation? P(t)y'' + Q(t)y' + R(t)y = S(t)

A: We have to solve for a linear equationPty''+Q(t)y'+R(t)y=S(t)

Q: 3. a) Define Integrating Factor and Exact Differential Equation. b) Solve: (x2 + xy-y² )dx+ x² - 2xy…

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

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: Q3: Solve the following differential: y" - 4y + 5y = x *******

A:

Q: If y = v3x , then y' is A. -1/2 B. V3 x -1/2 С. /3x V3 D. 2 V3 -1/2

A: Given y=3x

Q: Find a general solution of the equation: 3x?y" + 2xy' – 2y = 0

A:

Q: The rate of increase in a bank account is 4% of the amount in the account; the initial deposit is…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: Solve the following first order equations: (e" + y)dx + (2+x + ye")dy = 0, y(0) = 1.

A: First order linear differential equation

Q: Solve (yz + хуz) dx + (zx + хуz) dy + (ху + хуz) dz =

A:

Q: Identify the differential equation solved by y = e** a) Oy" – 9y + 20y = 0 b) Oy" + 9y' – 20y = 0 с)…

A: The solution is given as

Q: Find the general solution of the equation

A:

Q: a. Evaluate S dx α x2+βx+13

A: Given- ∫xαx2+βx+13dx To find- The value of the above integral. Identity Used- ∫1a2+x2=1atan-1xa and…

Q: solve

A:

Q: differential equation y = C, sin(5x + C2) as its general solution. a) Oy" – 25y = 0 b) Oy" + 25y = 0…

A:

Q: Find the order and the degree of the differential equation cos x COS X A 2,4 B) 5, 8 © 5,4 5,2

A:

Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

A:

Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: Solve the following 3rd order equation: y'"+2y"-y'-2y=0

A: First find roots then general solution..

Q: 2. у' %3D х3 — 2ху when x = 1 & y = 2

A: This is a problem of differential equation.  Here we will substitute the some of variable and then…