given y=1/x is a solution 2x^2 d2y/dx + xdy/dx - 3y = 0 , x>0 a) Find a linearly independent solution by reduction the order approach b) Show that 2 solutions are linearly independent c) Write a general solution

given y=1/x is a solution 2x^2 d2y/dx + xdy/dx - 3y = 0 , x>0 a) Find a linearly independent solution by reduction the order approach b) Show that 2 solutions are linearly independent c) Write a general solution

Question
Applications of integrals
asked 2021-02-26
given \(\displaystyle{y}=\frac{{1}}{{x}}\) is a solution \(\displaystyle{2}{x}^{{2}}{d}{2}\frac{{y}}{{\left.{d}{x}\right.}}+{x}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}-{3}{y}={0},{x}{>}{0}\)
a) Find a linearly independent solution by reduction the order approach
b) Show that 2 solutions are linearly independent
c) Write a general solution

Answers (1)

2021-02-27
image
image
image
image
0

Relevant Questions

asked 2021-06-05
Given \(\int_{2}^{5}f(x)dx=17\) and \(\int_{2}^{5}g(x)dx=-2\), evaluate the following.
(a)\(\int_{2}^{5}[f(x)+g(x)]dx\)
(b)\(\int_{2}^{5}[g(x)-f(x)]dx\)
(c)\(\int_{2}^{5}2g(x)dx\)
(d)\(\int_{2}^{5}3f(x)dx\)
asked 2021-05-23
Find the indefinite integral \(\int \ln(\frac{x}{3})dx\) (a) using a table of integrals and (b) using the Integration by parts method.
asked 2021-04-23
Suppose that x represents the larger of two consecutive odd integers.
a. Write a polynomial that represents the smaller integer.
b. Write a polynomial that represents the sum of the two integers. Then simplify.
c. Write a polynomial that represents the product of the two integers. Then simplify.
d. Write a polynomial that represents the difference of the squares of the two integers. Then simplify
asked 2021-02-05
A differential equation and a nontrivial solution f are given below. Find a second linearly independent solution using reduction of order. Assume that all constants of integration are zero.
\(tx''-(2t+1)x+2x=0,\ t>0,\ f(t)=3*e^{2t}\)
asked 2021-06-03
Evaluate each of the following integrals.
\(\int_{0}^{2}(x^{2}+2x-3)^{3}(4x+4)dx\)
asked 2021-05-08
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
\(\int_{0}^{3}\sin(x^{2})dx=\int_{0}^{5}\sin(x^{2})dx+\int_{5}^{3}\sin(x^{2})dxZKS
asked 2021-03-10

A system of linear equations is given below.
\(2x+4y=10\)
\(\displaystyle-{\frac{{{1}}}{{{2}}}}{x}+{3}={y}\)
Find the solution to the system of equations.
A. (0, -3)
B. (-6, 0)
C. There are infinite solutions.
D. There are no solutions.

asked 2021-04-02
Find all rational zeros of the polynomial, and write the polynomial in factored form.
\(\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}-{3}{x}^{{{2}}}-{2}{x}+{3}\)
asked 2021-03-03
Find all rational zeros of the polynomial, and write the polynomial in factored form.
\(\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}+{7}{x}^{{{2}}}+{4}{x}-{4}\)
asked 2021-01-28

Which of the following is an equation of the line that has a y-intercept of 2 and an x-intercept of 3?
(a) \(-2x + 3y = 4\)
(b) \(-2x + 3y = 6\)
(c) \(2x + 3y = 4\)
(d) \(2x + 3y = 6\)
(e) \(3x + 2y = 6\)

...