Cartesian equation of |z-i|=|z| is 1 yミ - 2 o y-2y=1 y-2y= - 1

Q: Solve Cauchy-Euler equation. a2y"-2y 2x %3D

A: (1) The equation is, x2y''-2y=2x Take y=xm Then take the derivative, y'=mxm-1 Take the derivative…

Q: Solve the equations to find x, y, z by Gaussian elimination : x-x+z =4 x + 3y-을-7 3 X -3 X y-4z 5

A:

Q: Solve the system of linear equations for x and y.(cos θ)x + (sin θ)y = 1(−sin θ)x + (cos θ)y = 0

A: (cos θ)x + (sin θ)y = 1              ------------Eqn (1) (−sin θ)x + (cos θ)y = 0…

Q: Find the solution of the equation 3U,-5U, =0 satisfying the condition U(0, y) = sin y

A:

Q: What are the roots of the auxiliary equation for a homogeneous linear equation with real, constant…

A: Follow next step

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

A:

Q: 3. Obtain two linearly independent solutions valid near the origin: 3xy" +(2-x)y' - 2y = 0

A: As per the question we are given the following second order ODE : 3xy’’ + (2-x)y’ - 2y = 0 And we…

Q: Differentiate the following linear and non-linear equations, and give a reason that why its linear…

A:

Q: Solve for all possible solution in the equation y^2 + y = x + Inx + e^y - x^2, using Secant Method *

A:

Q: Obtain the particular solution of (3x2 - 2y2)y' = 2xy; x =0, y=-1.

A: We have to solve

Q: Find the general solution to y'" + y = 0 Show the solution.

A:

Q: - Find the solution of the equation 3U, -5U, = 0 satisfying the condition U(0, y) = sin y

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

Q: Find solutions using Exact Equations 5. Solve (2t3 + 3y)dt + (3t + y – 1)dy = 0

A: Firstly Compare given differential equation with Mdt+Ndy then find the exactness of equation and…

Q: 54. yy' 2y2 = ex -

A:

Q: (y + 1)dx + (4x - y)dy 0

A: Explanation of the answer is as follows

Q: What are the roots of the auxiliary equation for a homogeneous linear equation with real, constant…

A: We have to solve the problem

Q: (2x + 3y + z = -1 Зх + Зу + z %3D1 (2x + 4y + z = -2 Give the solution of

A: We can find the answer using Gaussian elimination method as below.

Q: Solve the system of linear equations for x and y.(cos θ)x + (sin θ)y = 1 (−sin θ)x + (cos θ)y = 1

A:

Q: Let y(x) be the solution for the DE: y = (x+y+ 2)2 If y(0) = -2, then find y() %3D

A:

Q: The solution of y" = - y, y(0) = 1, y'(0) = 0 is %3D

A:

Q: 1nd the general and definite solutions of the diIference equations

A:

Q: Solve for Gaussian Elimination with Back Substitution. 2x+y+8z=-1 x-y+z=-2 3x-2y-2z=2

A:

Q: 3. Which equation passes through the point (1, -2) and is perpendicular to y = x O y = 3x - 1 O y =…

A:

Q: 5. Solve Equations 2x+y+z=5,3x+5y+2z=15,2x+y+4z=8 using Gauss Seidel method

A: Stape by Step solution given below.

Q: Find the solution to y - x+t y' = y if r(0) = 5 and y(0) = 4. %3D

A:

Q: y" – 2y' + y = 1+a? 2

A:

Q: How do I solve this Bernoulli equation using P(x), Q(x) and n as well as u(y)?

A: First, we write it in form of Bernoulli Differential equation.

Q: Find the general solution and the particular equation of the Equation Linear 2ª order given the…

A: We have to be find solution

Q: Find that solution of y’= 2(2x-y) which passes through the point (0,1). Use Linear Equation of Order…

A:

Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: a. Find that solution of y' = 2(2x-y) which passes through the point (0, 1). %3D

A: For part a). Given that                      y' = 2(2x-y) =4x-2y                      y' + 2y = 4x…

Q: 1 y" +y+y=x²-2x 4

A:

Q: Solve the linear system of equations using Differential Operator method... show details...…

A:

Q: 14. dQ/dt + (2/10 + 2t)Q = 4 2(5 + t)² + C 5+t

A:

Q: Convert y" – 3t y'+3 y=cos(5 t) into a system of first-order equations.

A: The given differential equation is                                             y''-3ty'+3y=cos(5t)

Q: %3D у — Зу + Зу - у %3D 4е" y y =

A:

Q: Particular solution of y' = x+xy²/4y, y(1) = 0

A: Given differential equation- y'=x+xy24y   , y(1)=0 We need to find particular solution of the given…

Q: Determine three linearly independent solutions to the equation y" + 2y" – 3y = 0 of the form y(x) =…

A: The given differential equation is                                                y'''+2y''-3y'=0

Q: Solve 5 2 E #(0) = – 2, y(0) = = 10 | Ly' - 29 - x(t) = %3D y(t) =

A:

Q: Solve the Cauchy-Euler equation: x*y' Зху + 4y = 0. %3D

A: Given Cauchy-Euler differential equation is

Q: utilize the characteristic equations method to solve the equation y''-5y'+3y=0 y(0)=3, y'(0)=-1

A:

Q: y (+zy'+y= ctDsint %3D

A: Given an ordinary non- homogenous differential equation : y(4)+2y'+y=(t+1)sint We need to find the…

Q: Consider the system {{ = - sin(x) (a) Find all the critical points (equilibrium solutions). (b) Find…

A: (a) Given system of equations are dxdt=y and dydt=-sinxthat is X'=AX where A=01-sinx0Critical points…

Q: (x2D2 - 3xD + 41)y = 0, y(1) = -n, y'(1) = 2n %3D

A:

Q: II. Homogeneous equations 1. (x² + y²)dy = 2xydx Ans: = Ax %3D %3D 1-

A:

Q: x' = -2x +y x(0) = -2 y(0) = 2 y' = -5x + 4y %3D

A:

Q: = -y² + 2x²y + 2x – xª, y1 = x² %3D

A: The Riccati equation is of the form

Q: -B-2-1 -2 -3- -8- 16+ hich equation best represents the linear functi Oy=-5x + % Dy= -5x+ 3 Dy= % x…

A:

Q: Find the Solution to Homogeneous LinearEquation: (D3-3D2-3D+1)y=0

A: Given equation is D3-3D2-3D+1y=0 find the solution of the given equation.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.