(1 point) We know that y(x) = ** is a solution to the differential equation y...
(1 point) We know that y(x) 72 is a solution to the differential equation Dy - Dy - 98y = 0 for 2 € (-00,00). Use the method of reduction of order to find the second solution to Dy - Dy - 98y = 0 for x € (-0,00) (a) After you reduce the second order equation by making the substitution w = ' you get a first order equation of the form f(x,x) = Note: Make sure you use...
(1 point) The differential equation dx has r4 as a solution. Applying reduction order we set Y2-uz" Then (using the prime notation for the derivatives) So, plugging 32 into the left side of the differential equation, and reducing, we get The reduced form has a common factor of r5 which we can divide out of the equation so that we have ru" + u0 Since this equation does not have any u terms in it we can make the substitution...
The indicated function y(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, re-SP(x) dx as instructed, to find a second solution y2(x). XY" + y = 0; Y- In x
The indicated function y_(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, e-SP(x) dx dx Y2 = Y1(x) >> (5) y? (x) as instructed, to find a second solution y2(x). x?y" + 2xy' – 6y = 0; Y=x2 Y2=
The indicated function yı() is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, Y2 = vy() / e-SP(x) dx dx (5) y?(x) as instructed, to find a second solution y2(x). x?y" + 2xy' – 6y = 0; Y1 = x2 Y2 The indicated function yı(x) is a solution of the given differential equation. 6y" + y' - y = 0; Y1 Fet/3 Use reduction of order or formula (5) in Section...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). y'' + 2y' + y = 0; y1 = xe−x y2 =
Find a second solution of the given differential equation y2(x). Use reduction of order or formula. y"- 6y'+25y =0; y1=23cos(4x)
Consider differential equation (x - 1)y" – xy' + y = 0. a). Show that yi = el is a solution of this equation. Use the method of reduction of order to find second linearly independent solution y2 of this equation. (2P.) b). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 1. c). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 0. d). Does your answer in b) and c)...
2) (25 points) a) (5 points) Verify that y= eat is a solution of the homogeneous differential equation y" - 12y' + 36 y = 0. b) (15 points) Use the method of reduction of order to find a second solution 72 of the given homogeneous equation and a particular solution y of the nonhomogeneous differential equation y" - 12y' + 36 y = 36. e) (5 points) Can you write the general solution of the nonhomogeneous differential equation y"...
Consider the homogeneous linear third order equation A) xy'''−xy'' + y'−y = 0 Given that y1(x) = e^x is a solution. Use the substitution y = u*y1 to reduce this third order equation to a homogeneous linear second order equation in the variable w = u'. You do not need to solve this second order equation. B.) xy''' + (1−x)y'' + xy'−y = 0. Given that y1(x) = x is a solution. Use the substitution y =...