Solution to a differential equation, Mathematics

Assignment Help:

A solution to a differential equation at an interval α < t < b is any function y (t) that satisfies the differential equation in question on the interval α < t < b.  It is significant to note that solutions are frequently accompanied through intervals and these intervals can impart several of significant information regarding the solution.  Consider the subsequent illustration.

Illustration 1:  Show that y(x) = x-3/2 is a solution to 4x2 y′′ + 12xy′ + 3 y = 0 for x > 0.

Solution: We'll require the first and second derivative to do this.

y'(x) = (-3/2) x-5/2                     y''(x) = (15/4) x-7/2

Plug these in addition to the function in the differential equation.

4x2 ((15/4) x-7/2) + 12x((-3/2) x-5/2) + 3(x-3/2) = 0


Related Discussions:- Solution to a differential equation

Complex number, a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.fi...

a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k

Continuity requirement, Continuity requirement : Let's discuss the continu...

Continuity requirement : Let's discuss the continuity requirement a little. Nowhere in the above description did the continuity requirement clearly come into play.  We need that t

Multiplying mixed numbers, Q. Multiplying Mixed Numbers? Ans. Mult...

Q. Multiplying Mixed Numbers? Ans. Multiplying mixed numbers is a 3-step process: 1. Convert the mixed numbers to improper fractions 2. Multiply the fractions 3.

How much area will it irrigate in 30 minutes , Water in a canal 30 dm wide ...

Water in a canal 30 dm wide and 12 dm deep is flowing with a velocity of 10 km/h. How much area will it irrigate in 30 minutes if 8 cm of standing water is required for irrigation?

Critical point of exponential functions and trig functions, Critical point ...

Critical point of exponential functions and trig functions, Let's see some examples that don't just involve powers of x. Example:  find out all the critical points for the

Truth criteria-nature of mathematics, Truth Criteria :  Consider the follo...

Truth Criteria :  Consider the following statements: i) Peahens (i.e., female peacocks) lay eggs around September. ii) Water boils at 100°C. iii) 5 divides 15 without lea

Evaluate the volume and surface area of a rectangular solid, Evaluate the v...

Evaluate the volume and surface area of a rectangular solid: Calculate the volume & surface area of a rectangular solid along with a =   3", b = 4", & c = 5".  Solution:

Probability, One coin is tossed thrice. what will be the probability of get...

One coin is tossed thrice. what will be the probability of getting neither 3 heads nor 3 tails

How to raise powers of monomials, How to raise Powers of Monomials ? To ...

How to raise Powers of Monomials ? To raise a monomial to a certain power: Step 1: Place the entire monomial inside parentheses, and place the desired power outside the paren

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