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Please help on these HW problems
It can be shown that yı = x-2, y2 =...
(1 point) It can be shown that yı = e-4x and y2 = xe-4x are solutions...
(1 point) It can be shown that yı = e-4x and y2 = xe-4x are solutions to the differential equation y + 8y +16y=0 on the interval (-00, 00). Find the Wronskian of yn y (Note the order matters) W(y1, y2) = Do the functions yn y form a fundamental set on (-00,00)? Answer should be yes or no
true or false If yı(t) and y2(t) are two solutions of the differential equation y2 –...
true or false
If yı(t) and y2(t) are two solutions of the differential equation y2 – y' +y = 0, then for any constants cı and c2, cıyı(t) + C2y2(t) is also a solution. Doğru Yanlış
1. (20 pts.) In the following Problems: (a) Seek power series solutions of the given differential...
1. (20 pts.) In the following Problems: (a) Seek power series solutions of the given differential equation about the given point xo ; find the recurrence relation. (b) Find the first four terms in each of two solutions yi and y2 (unless the series terminates sooner). (c) By evaluating the Wronskian W(y1, y2)(xo), show that yı and y2 form a fundamental set of solutions. (d) If possible, find the general term in each solution. i) y" +k+x+y = 0, 40...
(b) (30 points) Solve the following IVP given that yı (x) = x and y2 (x)...
(b) (30 points) Solve the following IVP given that yı (x) = x and y2 (x) = x3 are solutions to the corresponding homogeneous differential equation. Be sure to fully evaluate any integrals that arise. (You will have to use polynomial long division.) " - 3xy' + 3y = y(1) = 0, y(1) = 0 1+2
(1 point) It can be shown that h-e® and y2-e 9z are solutions to the differential...
(1 point) It can be shown that h-e® and y2-e 9z are solutions to the differential equation on the interval (-oo, oo) Find the Wronskian of y1,3/2 (Note the order matters) Do the functions y1, 32 form a fundamental set on -oo, 0o)? Answer should be yes or no
(1 point) The general solution of the homogeneous differential equation can be written as 2 where...
(1 point) The general solution of the homogeneous differential equation can be written as 2 where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation 2y 5ryy 18z+1 isyp so yax-1+bx-5+1+3x NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) 3, y'(1) 8 The fundamental theorem for linear IVPs shows that this solution is the unique solution to...
ďyi dx dx 1 Consider the following Ordinary Differential Equation (ODE) for function yı(x) on interval...
ďyi dx dx 1 Consider the following Ordinary Differential Equation (ODE) for function yı(x) on interval [0, 1] dyi dyi +(-4.7) * + 4.4 * +(-0.7) * yı(x) = -0.216. el.1-x dx dx2 with the following initial conditions at point x = 0: dyi dayı Yi = -0.316, = 6.2424, = 22.3846 dx2 Introducting notations dyi dy2 dy1 Y2 = Y3 = dx2 convert the ODE to the system of three first-order ODEs for functions yi, Y2, y3 in the...
d'yi dạy1 Yi = 0.5 Consider the following Ordinary Differential Equation (ODE) for function yı (2)...
d'yi dạy1 Yi = 0.5 Consider the following Ordinary Differential Equation (ODE) for function yı (2) on interval [0, 1] dyi +(-4.9) * + 7.9 * +(-4.2) * yı(x) = -0.2 - 1.0-2 dx3 d.x2 dc with the following initial conditions at point x = 0: dy1 dạyi = 2.48 = 6.912 dc d.2 Introducting notations dyi dy2 day1 Y2 = y3 = da dc d.x2 convert the ODE to the system of three first-order ODEs for functions yi, y2,...
A) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t...
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of the O.D.E.? C) State the general solution for this O.D.E.
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of...
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2,...
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2, roots of the characteristic polynomial of the equation above. 11,12 M (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) M y2(t) = M (C) Find the Wronskian of the fundamental solutions you found in part (b). W(t) M (d) Use the fundamental solutions you found in (b) to find functions ui and Usuch...
(1 point) It can be shown that yı = e-4x and y2 = xe-4x are solutions to the differential equation y + 8y +16y=0 on the interval (-00, 00). Find the Wronskian of yn y (Note the order matters) W(y1, y2) = Do the functions yn y form a fundamental set on (-00,00)? Answer should be yes or no
true or false
If yı(t) and y2(t) are two solutions of the differential equation y2 – y' +y = 0, then for any constants cı and c2, cıyı(t) + C2y2(t) is also a solution. Doğru Yanlış
1. (20 pts.) In the following Problems: (a) Seek power series solutions of the given differential equation about the given point xo ; find the recurrence relation. (b) Find the first four terms in each of two solutions yi and y2 (unless the series terminates sooner). (c) By evaluating the Wronskian W(y1, y2)(xo), show that yı and y2 form a fundamental set of solutions. (d) If possible, find the general term in each solution. i) y" +k+x+y = 0, 40...
(b) (30 points) Solve the following IVP given that yı (x) = x and y2 (x) = x3 are solutions to the corresponding homogeneous differential equation. Be sure to fully evaluate any integrals that arise. (You will have to use polynomial long division.) " - 3xy' + 3y = y(1) = 0, y(1) = 0 1+2
(1 point) It can be shown that h-e® and y2-e 9z are solutions to the differential equation on the interval (-oo, oo) Find the Wronskian of y1,3/2 (Note the order matters) Do the functions y1, 32 form a fundamental set on -oo, 0o)? Answer should be yes or no
(1 point) The general solution of the homogeneous differential equation can be written as 2 where a, b are arbitrary constants and is a particular solution of the nonhomogeneous equation By superposition, the general solution of the equation 2y 5ryy 18z+1 isyp so yax-1+bx-5+1+3x NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y(1) 3, y'(1) 8 The fundamental theorem for linear IVPs shows that this solution is the unique solution to...
ďyi dx dx 1 Consider the following Ordinary Differential Equation (ODE) for function yı(x) on interval [0, 1] dyi dyi +(-4.7) * + 4.4 * +(-0.7) * yı(x) = -0.216. el.1-x dx dx2 with the following initial conditions at point x = 0: dyi dayı Yi = -0.316, = 6.2424, = 22.3846 dx2 Introducting notations dyi dy2 dy1 Y2 = Y3 = dx2 convert the ODE to the system of three first-order ODEs for functions yi, Y2, y3 in the...
d'yi dạy1 Yi = 0.5 Consider the following Ordinary Differential Equation (ODE) for function yı (2) on interval [0, 1] dyi +(-4.9) * + 7.9 * +(-4.2) * yı(x) = -0.2 - 1.0-2 dx3 d.x2 dc with the following initial conditions at point x = 0: dy1 dạyi = 2.48 = 6.912 dc d.2 Introducting notations dyi dy2 day1 Y2 = y3 = da dc d.x2 convert the ODE to the system of three first-order ODEs for functions yi, y2,...
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of the O.D.E.? C) State the general solution for this O.D.E.
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of...
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2, roots of the characteristic polynomial of the equation above. 11,12 M (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) M y2(t) = M (C) Find the Wronskian of the fundamental solutions you found in part (b). W(t) M (d) Use the fundamental solutions you found in (b) to find functions ui and Usuch...
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