Differential Equations:Obtain the differential equation of the family of curves, parabolas with vertex and focus on the y-axis.а. (х- у)у" — у'3 — у? — у' — 13D0b. (x - у)? (у* + 1) 3 (x + yy)?с. ху" — у' %3D 0d. хуу" + ху? —у' %3D 0

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Answered: Differential Equations: Obtain the…

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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Find the Differential Equation
Determine the particular solution of the ODE y" + Inx = -1 a. (-0.5x * Inx) + 0.25x b. None of the choices O c. (0.5x * Inx) - 0.25x O d. (-0.5x^2 * Inx) + 0.25x^2 е. (0.5х^2 * Inх)- 0.25х^2
Solve by Guess-and-Check (Diff. Equations)
2. Centered-difference formula for the second derivative with two independent variables r and y a?u (x, y) = и(х+h.у ) — 2и(х,у)+и(х-h-у) и (§ , y ) 12 ax4 h? a²u (x , y) = h² a+u - (1 , η ) 12 əy4 и(x.y+h) — 2u(х .у) +и(х.у-h) where { E (x – h,x + h) and 7 E (y – h, y + h).
Consider the differential equation y'= -2x (A) At the point (1, -1), the direction field has a slope of (B) At the point (-1, 1), the direction field has a slope of (C) Along the x-axis the slope of the direction field is equal to which number or expression? (D) Along the y-axis the slope of the direction field is equal to which number or expression? (E) Use your answers above to help choose the correct direction field for the differential equation. 1 ✓ 2 1 CAI -1- Ō 151 X / 1 / 11 1 1 / // -1 1|1 1 N Q 2 2 NN NIX V NN / / / 17 1 +5/ -17 -1 21 1 4342 V N / // 1 Q f 1 775 \ \\ \ \-1 + \\\' 1 1 1 1 1 1 1 1 2 J 1 / 1 / 1 1 1 1 7 +71 I -1 / / 1-1 / / - \ \ 1 / /-1- \ // +1 OF I 1- / 4 ¹1 111 7 1 a
Which one of the following is the Exact differential equation ? ㅇ (교2 +3ary)dy + (1y' + z®)dz = 0 (22 + 3zy)dy + (y?+ 능교2)dz=D0 ㅇ (22 + 3zy)dz + (y' + 교2)dy=0 (교2 +3zg)dz + (y'+ 교)dy= 0 2
Differential Equation, Ty!
The solution of the form (see equation) is the particular solution proposed for the differential equation:

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Differential Equations: Obtain the differential equation of the family of curves, parabolas with vertex and focus on axis. а. (х - у)у" — у'з — у? — у' — 1%3о b. (x – y)² (y'² + 1) = (x + yy')² c. xy" – y' = 0 d. хуу" + ху? —- уу' %— 0