=> (x² - 6x) y - y = 0 Find the singular point and ordinary point...
Exercise 7.3.101: In the following equations classify the point x = 0 as ordinary, regular singular, or singular but not regular singular. a) y" + y = 0 b) x3y" + (1 + x)y = 0 c) xy" + x y' + y = 0 d) sin(x)y" - y = 0 e) cos(x)y” – sin(x)y = 0
Exercise 7.3.8. In the following equations classify the point x = 0 as ordinary, regular singular, or singular but not regular singular. a. 2²(1+x?)y" + xy = 0 b. x+y" + y' +y=0 C. ng” +cº+y= 0 d. xy" + xy' - e"y=0 e. a’y" + xạy' + xạy=0
1. (x2-5x)y”-yʻ- y=0 Find the ordinary and singular points of the differential equation.
find all singular and ordinary points of following differential equation (x2_5x)y"-yl-y=0
Given the DE: y"-(x+1)y'-y=0 use it to answer the following: a) Find the singular point(s), if any, and if lower bound for the radius of convergence for a power series solution about the ordinary points x=0 b)The recurrence relation Hint: It will be a 3-term recurrence relation c)Give the first four non-zero terms of each of the two linearly independent power series solutions near the ordinary point x=0
show that the equation xy"+y'-y=0 has a regular singular point at x=0, find the indicial equation and its roots how many independent solutions does the equation have ?
Identify Singular points of the DE: (x2 - 9) y" + 2xy' + (Inx) y = 0 x = £3 are Singular points x = £3 and all x < 0 are Singular points. O None of them All x > 0 are Singular points Identify Ordinary points of the DE: (x2 - 2x + 5) y" + 2xy' + (x - 1)y=0 O x = 1 + 2i are Ordinary points. None of them O x > 0 are...
IV. If x = 0 is a regular singular point, find the exponent of the differential equation at x = 0 (find only a value ofr): x2y" + (6 sin x)y' + 6y = 0.
(1 point) 6y 6xe-6x, 0 < x < 1 with initial condition y(0) = 2. Given the first order IVP y 0, х21 (1) Find the explicit solution on the interval 0 < x < 1 У(х) %3 (2) Find the lim y(x) = х—1 (3) Then find the explicit solution on the interval x 1 У(х) —
The definitions for ordinary and regular singular point that we have given only apply if ro is finite. Sometimes it is necessary to look at the behaviour of the solution near infinity. This is 0 done by changing variables = 1/x and studying the resulting equation about a) Make this substitution into the following DE a(a)y" b(r)c(x)y = 0, independent variable Ç and rewrite it entirely in terms of the new b) What conditions do you require for to be...