Homework Answers
with
the help of the given solution we solve this problem. Satisfing the
solution in the given equation we get the values of 
and 
.
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x...
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x > 0 of the form Yi = x n=0 where co = 1. Enter r = -2 Cn = - n= 1,2,3,...
(1 point) Find the solution of cºy" + 5xy' + (4 - 4x)y = 0, 2...
(1 point) Find the solution of cºy" + 5xy' + (4 - 4x)y = 0, 2 > 0 of the form 00 yi =T n0 where co 1. Enter T= Cn = n = 1,2,3,...
(1 point) Find the solution of x²y" + 5xy' + (4 – 3x) y = 0,...
(1 point) Find the solution of x²y" + 5xy' + (4 – 3x) y = 0, x > 0 of the form y=x" Wazek, k=0 where ao = 1. r = help (numbers) ak = , k=1,2,3,... help (formulas)
1. Given the piece-wise function, 3x if x < 0 f(x)=x+1 if 0 < x 52...
1. Given the piece-wise function, 3x if x < 0 f(x)=x+1 if 0 < x 52 :- 2)2 if x>2 Evaluate f (__); f(0); f (); f(5)
Consider the system of equations dxdt=x(3−x−4y) dydt=y(1−3x), taking (x,y)>0. (1 point) Consider the system of equations...
Consider the system of equations dxdt=x(3−x−4y) dydt=y(1−3x),
taking (x,y)>0.
(1 point) Consider the system of equations de = 2(3 – 2 – 49) = y(1 - 33), taking (2,y) > 0. (a) Write an equation for the (non-zero) vertical (-)nullcline of this system: (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: (Enter your equation, e.g. y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria =...
For the following Euler-Cauchy equation: x2y" + axy + by = 0 a) Show that y(x)-xrnis...
For the following Euler-Cauchy equation: x2y" + axy + by = 0 a) Show that y(x)-xrnis a solution where mis equal to m -(1-a) | (1-а)2-b b) Show that for the case when ^1 -a)2 - b 0, the general solution is equal to 4. 4 1-a y(x) = x-2-(G + c2 In x) c) Solve the following problem x2y"-5xy' + 9y-0, y(1)-0.2, y'(1)-0.3 d) Show that for the case when-(1-a)2-b 〈 0, the general solution is equal to 1-а...
3. [10pts] Consider the DE: xy" + 7xy' + Ty = 0. (a) Find the roots...
3. [10pts] Consider the DE: xy" + 7xy' + Ty = 0. (a) Find the roots rı and r2 of the indicial equation of the DE (with rı >r2). r = r2 = Solution: (b) If we use Frobenius method to solve the DE, we obtain for the largest indicial root and for n > 0, a recurrence acn relation of the form Cn+1 where a and b are constants. Find a and b. m11
Consider the differential equation (1-x²)y" - 5xy' - 3 y = 0 1. Find its general...
Consider the differential equation (1-x²)y" - 5xy' - 3 y = 0 1. Find its general solution y = Xar, x" in the form y = doy1(x) + anyz(x), where yı(x) and y2(x) are power series 2. What is the radius of convergence for the series yı(x) and y(x)?
Could someone explain how these to get these phase portraits by hand with ẋ=y and ẏ=ax-x^2...
Could someone explain how these to get these phase portraits by
hand with ẋ=y and ẏ=ax-x^2 especially for a=0 case where you have
eigenvalues all equal to zero?
6.5.4 a>0 Sketch the phase portrait for the system x = ax-x, for a < 0, a = 0, and For a -(0 We were unable to transcribe this imageFor a>0 ES CS
consider the DE: y''+x2y'+x2y=0 about the ordinary point x=0 a) find the recurrence relation, and indicate...
consider the DE: y''+x2y'+x2y=0 about the ordinary point x=0 a) find the recurrence relation, and indicate if any of the coefficients are equal to zero .(if any) b) use the recurrence relation to write the first four nonzero terms of each of the two linearly independent power series near the ordinary point x=0. My attempt... after plugging in the y, y' , and y'' power series. I got something that looked like 2a2+6a3x + sigma from n=2 -> to infinity...
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x > 0 of the form Yi = x n=0 where co = 1. Enter r = -2 Cn = - n= 1,2,3,...
(1 point) Find the solution of cºy" + 5xy' + (4 - 4x)y = 0, 2 > 0 of the form 00 yi =T n0 where co 1. Enter T= Cn = n = 1,2,3,...
(1 point) Find the solution of x²y" + 5xy' + (4 – 3x) y = 0, x > 0 of the form y=x" Wazek, k=0 where ao = 1. r = help (numbers) ak = , k=1,2,3,... help (formulas)
1. Given the piece-wise function, 3x if x < 0 f(x)=x+1 if 0 < x 52 :- 2)2 if x>2 Evaluate f (__); f(0); f (); f(5)
Consider the system of equations dxdt=x(3−x−4y) dydt=y(1−3x),
taking (x,y)>0.
(1 point) Consider the system of equations de = 2(3 – 2 – 49) = y(1 - 33), taking (2,y) > 0. (a) Write an equation for the (non-zero) vertical (-)nullcline of this system: (Enter your equation, e.g., y=x.) And for the (non-zero) horizontal (y-)nullcline: (Enter your equation, e.g. y=x.) (Note that there are also nullclines lying along the axes.) (b) What are the equilibrium points for the system? Equilibria =...
For the following Euler-Cauchy equation: x2y" + axy + by = 0 a) Show that y(x)-xrnis a solution where mis equal to m -(1-a) | (1-а)2-b b) Show that for the case when ^1 -a)2 - b 0, the general solution is equal to 4. 4 1-a y(x) = x-2-(G + c2 In x) c) Solve the following problem x2y"-5xy' + 9y-0, y(1)-0.2, y'(1)-0.3 d) Show that for the case when-(1-a)2-b 〈 0, the general solution is equal to 1-а...
3. [10pts] Consider the DE: xy" + 7xy' + Ty = 0. (a) Find the roots rı and r2 of the indicial equation of the DE (with rı >r2). r = r2 = Solution: (b) If we use Frobenius method to solve the DE, we obtain for the largest indicial root and for n > 0, a recurrence acn relation of the form Cn+1 where a and b are constants. Find a and b. m11
Consider the differential equation (1-x²)y" - 5xy' - 3 y = 0 1. Find its general solution y = Xar, x" in the form y = doy1(x) + anyz(x), where yı(x) and y2(x) are power series 2. What is the radius of convergence for the series yı(x) and y(x)?
Could someone explain how these to get these phase portraits by
hand with ẋ=y and ẏ=ax-x^2 especially for a=0 case where you have
eigenvalues all equal to zero?
6.5.4 a>0 Sketch the phase portrait for the system x = ax-x, for a < 0, a = 0, and For a -(0 We were unable to transcribe this imageFor a>0 ES CS
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