Determine whether the given first-order differential equation is linear in the indicated dependent variable by matching it with the differential equation given in (7)dyin Section 1.1, a₁(x) dx + ²(x) = g(x).linear or non linear(y³ - 1) dx + x dy = 0; in y; in xThe differential equation is --Select--in y and ---Select--in x.linear or non linear

We have to check whether given differential equation is linear in x or y.

Answered: Determine whether the given first-order…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A certain differential equation has the form f(x)dx + g(x)h(y)dy = 0. with none of the functions f(x), g(x), h(y) identically 0. Show that a necessary and sufficient condition for this equation to be exact is that g(x) = constant.
State the order of the given ordinary differential equation. (1-x)y" - 9xy' + 2y = cos x Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. dny an(x) dxn + a "n - 1(x). an-ly dxn-1 - + ... + a₁(x) dx + a (x)y = g(x) (6) dx linear O nonlinear
Put the given differential equation into form (3) in Section 6.3 (x − x0)2y'' + (x − x0)p(x)y' + q(x)y = 0 (3) for each regular singular point of the equation. Identify the functions p(x) and q(x). (x2 − 1)y'' + 4(x + 1)y' + (x2 − x)y = 0 (p(x),q(x))=( ? ) (smaller X0-value) (p(x),q(x))=( ? ) (Larger X0-value)
Part I Verify that each given function is a solution of the differential equation. y. (1)=e' y (1) =e y = 3t +r y, (1)=cosht y: (1)=e a. y"-y'=0 ; b. y"+2y'-3y= 0 c. ーy=r: d. y""+ 4y"+3y=t (1)=c" + e. 21 y"+3ty'-y=0, t>0 f. ty"+5ty'+ 4y 0, t>0 : 00 y(1) =e" ['e*ds+e i. y'=- *+y = 25 : j. 2y'+ y = 0 ; y=e2 6 6 y ==--e 5 5 dy k. + 20y = 24 dt 1. y"-6y'+13y=0 m. (y-x)y'=y-x+8 ; n. y'= 25+ y o. 2y'= y' cos x y = e" cos 2x y = x+4x+2 y =5 tan 5x -1/2 y=(1-sin.x)2
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, as instructed, to find a second solution y2(x).
The indicated function y₁(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, e-/P(x) dx V₂ = V₁(x) [² Y₂ = y} (x) dx (5) as instructed, to find a second solution y₂(x). (1 - 2x - x²)y" + 2(1+x)y' - 2y = 0; y₁ = x + 1
デジタル形式で段階的に解決ありがとう!! SOLVE STEP BY STEP IN DIGITAL FORMAT Determine the differential equation whose general solution is y = Cx. Also, obtain and graph the equation of the curve that passes through a) (1,2) and b) (-1,2)
State the order of the given ordinary differential equation. d²u du dr² dr + + u = cos(r + u) Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. + an- + + a an(x) any dxn 1 (x) an-ly + a₁(x)dy + a(x) = g(x) (6) dxn-1 linear nonlinear

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