Question

In: Math

The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...

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). x2y'' − xy' + 26y = 0; y1 = x sin(5 ln(x)).......................................

Solutions

Expert Solution


milcah answered 2 years ago
Next > < Previous

Related Solutions

The indicated function y1(x) is a solution of the given differential equation. Use reduction of order...
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order to find y2(x) x2y'' − xy' + 17y = 0 ;   y1=xsin(4In(x))
Topic: Differential Equations; reduction order. The indicated fuction y1(x) is a solution of the given differential...
Topic: Differential Equations; reduction order. The indicated fuction y1(x) is a solution of the given differential equation. Use the reduction order technique to find a second solution y2(x). xy'' + y' = 0;    y1= ln(x) Please, explain deeply each part of the solution, and include complete algebraic explanation as well. Otherwise, the answer will be negatively replied.
The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of...
The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y2(x) of the homogeneous equation and a particular solution yp(x) of the given nonhomogeneous equation. y'' − 3y' + 2y = x;    y1 = ex y2(x) = e^2x    yp(x) =   
Problem 3: Find a second solution by reduction of order - nonhomogeneous The given function y1(x)...
Problem 3: Find a second solution by reduction of order - nonhomogeneous The given function y1(x) is a solution of the associated homogeneous equation. Use the reduction of order method to find a solution y(x) = u(x)y1(x) of the nonhomogeneous equation. 1. x^2y'' + xy'−4y = x^3, y1 = x^2 2. 2x^2*y'' + 3xy'−y = 1/x ,    y1 = x^(1/2)
Verify that the indicated family of functions is a solution of the given differential equation. Assume...
Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d^2y/ dx^2 − 6 dy/dx + 9y = 0;    y = c1e3x + c2xe3x  When y = c1e3x + c2xe3x, dy dx = d2y dx2 =   . Thus, in terms of x, d^2y/dx^2− 6 dy/dx + 9y = + 9(c1e3x + c2xe3x) =   . 2) In this problem, y = c1ex + c2e−x is a two-parameter family...
Consider the following differential equation: x2y"-2xy'+(x2+2)y=0 Given that y1=x cos x is a solution, find a...
Consider the following differential equation: x2y"-2xy'+(x2+2)y=0 Given that y1=x cos x is a solution, find a second linearly independent solution to the differential equation. Write the general solution.
Find a particular solution of the given differential equation. Use a CAS as an aid in...
Find a particular solution of the given differential equation. Use a CAS as an aid in carrying out differentiations, simplifications, and algebra. y(4) + 2y'' + y = 11 cos(x) − 12x sin(x)
Use the one solution given below to find the general solution of the differential equation below...
Use the one solution given below to find the general solution of the differential equation below by reduction of order method: (1 - 2x) y'' + 2y' + (2x - 3) y = 0 One solution: y1 = ex
Use the method of reduction of order to find a second solution y2 of the given...
Use the method of reduction of order to find a second solution y2 of the given differential equation such that {y1, y2} is a fundamental set of solutions on the given interval. t2y′′ +2ty′ −2y=0, t > 0, y1(t)=t (a) Verify that the two solutions that you have obtained are linearly independent. (b) Let y(1) = y0, y′(1) = v0. Solve the initial value problem. What is the longest interval on which the initial value problem is certain to have...
In reduction of order, we take a homogeneous solution y1, then consider a potential solution y=uy1,...
In reduction of order, we take a homogeneous solution y1, then consider a potential solution y=uy1, When this is substituted into the second order DE, something important MUST happen for this technique to work. Explain what that important thing is.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT