Consider the following. x' = 6x − 10y y' = 10x − 6y, X(0) = (6, 10) (a) Find the general ...
Consider the following.
| x' | = | 6x − 10y |
| y' | = | 10x − 6y, X(0) = (6, 10) |
(a) Find the general solution.
(x(t), y(t)) =
 |
Determine whether there are periodic solutions. (If there are
periodic solutions, enter the period. If not, enter NONE.)
(b) Find the solution satisfying the given initial condition.
(x(t), y(t)) =
 |
 |
(c) With the aid of a calculator or a CAS graph the solution in
part (b) and indicate the direction in which the curve is
traversed.
 |
 |
 |
 |
Homework Answers
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Consider the following. x' = 6x − 10y y' = 10x − 6y, X(0) = (6, 10) (a) Find the general ...
Consider the following. x 12x - 13y y' = 13x - 12y, X(0) - (12, 13)...
Consider the following. x 12x - 13y y' = 13x - 12y, X(0) - (12, 13) (a) Find the general solution (xce), y(t) =( Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) NONE X (b) Find the solution satisfying the given initial condition. (x(C), y(0)) (c) with the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve it...
Consider the following. x = 8x + y y' - 2x + 6y. X(O) = (-1,2)...
Consider the following. x = 8x + y y' - 2x + 6y. X(O) = (-1,2) (a) Find the general solution (x(t), y(t) = Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) NONE (b) Find the solution satisfying the given initial condition (x(6), y(t)) - (c) With the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve is...
(1 point) 6y 6xe-6x, 0 < x < 1 with initial condition y(0) = 2. Given...
(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) —
x'-y,y 10x-7y using the method of elimination. 2) a) Find the general solution to b) What...
x'-y,y 10x-7y using the method of elimination. 2) a) Find the general solution to b) What happens to all solutions as ? You should find that all solutions approach the same point (x, y). This is an example of a fixed point. c) Find the particular solution to the IVP consisting of the above system of equations and the conditions x(0)2, y(0)-7
B5. Find the general solution of x' = 2x + 6y + et y' = x...
B5. Find the general solution of x' = 2x + 6y + et y' = x + 3y – e'.
Question 3 Find the general solution of "" - 6y" + 117' - 6-0 given that...
Question 3 Find the general solution of "" - 6y" + 117' - 6-0 given that r1 = 2 is a root of the characteristic equation a)y=C22*+&+603 b) y=,22+*+ Cre" c)y=C22*+&+C22 d) -Ce2+Ce*+6633 e)y=e 28+ Ce*+C, f) None of the above. Question 4 Find the general solution of "" – 3y" - Dy' + 27y=0 given that rı = -3 is a root of the characteristic equation. a) y=C2*+Cxé* +22 b) y=Ge4+Ce**,62* c) y= 3 + x +c, d) y=C+*+Cre*+,231...
Find the general solution of the DE: y’’(x) + 6y’(x) + 8y(x) = 3e^(-2x) + 2x
Find the general solution of the DE:
y’’(x) + 6y’(x) + 8y(x) = 3e^(-2x) + 2x
Please do 1a 1b 1d thanks Assuming x > 0, find the general solution of the...
Please do 1a 1b 1d thanks
Assuming x > 0, find the general solution of the following Euler equa- tions. a) x²y" – 3xy' +4y=0 (b)x²y" – 5xy +10y=0 f) 5x2y" + 12. y' + 2y = 0 g) x²y" + xy = 0 1. Assuming 2 > 0, find the general solution of the following Euler equa- tions. a) " - 3xy' + 4y = 0 b) – 5xy +10g = 0 c) 6x²y" + 7xy' - y =...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
Find the general solution of the given differential equation. x y - y = x2 sin(x)...
Find the general solution of the given differential equation. x y - y = x2 sin(x) y(x) = (No Response) Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) (No Response) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.) (No Response)
Consider the following. x 12x - 13y y' = 13x - 12y, X(0) - (12, 13) (a) Find the general solution (xce), y(t) =( Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) NONE X (b) Find the solution satisfying the given initial condition. (x(C), y(0)) (c) with the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve it...
Consider the following. x = 8x + y y' - 2x + 6y. X(O) = (-1,2) (a) Find the general solution (x(t), y(t) = Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) NONE (b) Find the solution satisfying the given initial condition (x(6), y(t)) - (c) With the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve is...
(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) —
x'-y,y 10x-7y using the method of elimination. 2) a) Find the general solution to b) What happens to all solutions as ? You should find that all solutions approach the same point (x, y). This is an example of a fixed point. c) Find the particular solution to the IVP consisting of the above system of equations and the conditions x(0)2, y(0)-7
B5. Find the general solution of x' = 2x + 6y + et y' = x + 3y – e'.
Question 3 Find the general solution of "" - 6y" + 117' - 6-0 given that r1 = 2 is a root of the characteristic equation a)y=C22*+&+603 b) y=,22+*+ Cre" c)y=C22*+&+C22 d) -Ce2+Ce*+6633 e)y=e 28+ Ce*+C, f) None of the above. Question 4 Find the general solution of "" – 3y" - Dy' + 27y=0 given that rı = -3 is a root of the characteristic equation. a) y=C2*+Cxé* +22 b) y=Ge4+Ce**,62* c) y= 3 + x +c, d) y=C+*+Cre*+,231...
Find the general solution of the DE:
y’’(x) + 6y’(x) + 8y(x) = 3e^(-2x) + 2x
Please do 1a 1b 1d thanks
Assuming x > 0, find the general solution of the following Euler equa- tions. a) x²y" – 3xy' +4y=0 (b)x²y" – 5xy +10y=0 f) 5x2y" + 12. y' + 2y = 0 g) x²y" + xy = 0 1. Assuming 2 > 0, find the general solution of the following Euler equa- tions. a) " - 3xy' + 4y = 0 b) – 5xy +10g = 0 c) 6x²y" + 7xy' - y =...
5. Repeat the same questions in 4.) for the ODE Py"- tt+2)y+(t+2)y2t3, (t>0) (a) Find the general solution of the homogeneous ODE y"- 5y +6y 0. Particularly find yi and (b) Find the equivalent nonhomogeneous system of first order with the chan of variable y (c) Show that (nvand 2( re solutions of the homogeneous system of ODEs (d) Find the variation of parameters equations that have to be satisfic 1 for y(t) vi(t)u(t) + (e) Find the variation of...
Find the general solution of the given differential equation. x y - y = x2 sin(x) y(x) = (No Response) Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) (No Response) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.) (No Response)
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