Method of reduction of order, Mathematics

Assignment Help:

Consider the equation

x2y′′+ xy′- y = 4x ln x

(a) Verify that x is a solution to the homogeneous equation.

(b) Use the method of reduction of order to derive the second solution to the homogeneous equation as Cx-1

(c) Use the method of variation of parameters to show that the general solution of the equation can be written as

y = x(ln x)2- x ln x + c1x + c2x-1


Related Discussions:- Method of reduction of order

Green function, greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t...

greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t,s)= {1-s for t or equal to s

Calculus , Mean, variance, skewness and kurtosis of a probability density f...

Mean, variance, skewness and kurtosis of a probability density function f(r)that has a distribution of a passive scalar filed in a stationary isotropic turbulence for initial condi

Project, report on shares and dividend using newspaper

report on shares and dividend using newspaper

Explain basic geometric concepts, Explain Basic Geometric Concepts ? P...

Explain Basic Geometric Concepts ? Points, lines, and planes are the most fundamental concepts in the study of geometry. Points A point has no length, width or heig

Calculate annual interest rate, 1. What is the present value of a security ...

1. What is the present value of a security that will pay $15,000 in 15 years if securities of equal risk pay 8.9% annually? Round your answer to the nearest cent. 475,858.20

Rectilinear figures, Q1- different types of rectilinear figures? Q2- interi...

Q1- different types of rectilinear figures? Q2- interior and exterior angles of the polygon? Q3-relation between interior and exterior angles of polygons? Q4- properties of any fiv

Simple derivatives, Simple derivatives Example   Differentiate followin...

Simple derivatives Example   Differentiate following.  (5x 3   - 7 x + 1) 5 ,[ f ( x )] 5 ,[ y ( x )] 5 Solution: Here , with the first function we're being asked to

Small samples-estimation of population mean , Estimation of population mean...

Estimation of population mean If the sample size is small (n In this case Population mean µ = x¯ ±  tS x¯  x¯ = Sample mean S x¯ =  s/√n S = standard deviation

Parallel and perpendicular lines, The last topic that we have to discuss in...

The last topic that we have to discuss in this section is that of parallel & perpendicular lines. Following is a sketch of parallel and perpendicular lines. Suppose that th

Parabola, If the point (a,2a) is an interior point of the region bounded by...

If the point (a,2a) is an interior point of the region bounded by the parabola y2=16x and the double ordinate through the focus then a belongs to

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd