solve the homogeneous/separable de 5. (y+√√x²+ y²)dx - xdy =when x = √3, y = 1I

The given homogeneous differential equation can be solved by putting y=vx

Answered: (y + √√√x² + y²)dx-xdy = 0 x2 when x =…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Use the reduced order formula to find the second solution of the quation, xy"+y'=0; y1=Inx
Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1, y=2 2(xdx+ydy)=7(xdy+ydx)
Select all equations that are equivalent to a6z = 16. +623D16. a 2' +62 9=0 b. +6x +9= 16 +6x + 9= 25 Od (2+3)= 0 Oe (2 +3) = 16 Of (2 + 3) = 25
I asked ChatGPT to solve the second order linear non-homogeneous equation y"+2y+y= = 2x Is the solution that ChatGPT offers correct, or is there one or more mistakes in the work? If the work is correct, verify the solution. If it is incorrect, identify the exact place(s) where the mistake(s) occur. Explain your answer clearly! Below is the response from ChatGPT: Yes, I can solve the equation y"+2y+y = 2x. One way to solve it is to use the characteristic equation method. To find the characteristic equation, we set the left side of the equation to zero and solve for the roots of the characteristic equation, which is given by: r² + 2r + 1 = 0 Solving for the roots, we get: r₁=1+√-1-4--1+√-5 and r₂ =-1-√√-1-4 =-1-√√-5 So the roots are complex conjugates, which means the general solution of the homogeneous equation will be of the form: Yn(x) = e¯² (c₁ cos ( √5x) + ₂ sin (√5. x)) Where c₁ and c₂ are arbitrary constants. To find a particular solution, we can use the method of undetermined…
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Eliminate the arbitrary constant for y = 4 + Cje3 %3D Oy' + 3y + 12 = 0 Oy' - 3y + 12 = 0 %3D O y" – 3y + 12 = 0 %3D O y" + 3y +12 = 0

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(y + √√√x² + y²)dx-xdy = 0 x2 when x = √3, y = 1 I