Actual solution to a differential equation, Mathematics

Assignment Help:

The actual solution is the specific solution to a differential equation which not only satisfies the differential equation, although also satisfies the specified initial conditions.

Illustration: What is the actual solution to the subsequent IVP?

2ty' + 4y = 3;    y(1) = -4

Solution: This is in fact easier to do than this might at first appear. From the earlier illustration we already identify that differential equations have all solutions are of the form:

y(t) = 3/4 + c/t2

All that we require to do is find out the value of c that will provide us the solution that we're after. To determine this all we require do is utilize our initial condition that are given as:

-4 = y(1) = 3/4 + c/12

c= -4 -3/4 = -19/4

Thus, the actual solution to the Initial Value Problem is:

y(t) = ¾ - 19/4t2

From this last illustration we can notice that once we have the general solution to a differential equation determining the actual solution is nothing more than applying the initial conditions and resolving for the constants which are in the general solution.


Related Discussions:- Actual solution to a differential equation

Sequence and series, Find the sum og series 1+(1+3)+(1+3+5)+.......+(1+3+.....

Find the sum og series 1+(1+3)+(1+3+5)+.......+(1+3+...+15+17)=

Retail price index, Retail price index This is weighted average of pri...

Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp

The shortest distance between the line y-x=1 and curve x=y^2, Any point on ...

Any point on parabola, (k 2 ,k) Perpendicular distance formula: D=(k-k 2 -1)/2 1/2 Differentiating and putting =0 1-2k=0 k=1/2 Therefore the point is (1/4, 1/2) D=3/(32 1/2

Dynamic and kinematic viscosity , Tabulated values of the dynamic and kinem...

Tabulated values of the dynamic and kinematic viscosity of aqueous sodium chloride solutions have been researched in the academic literature (Kestin et al 1981). The data availab

Straight Line, can i known the all equations under this lesson with explana...

can i known the all equations under this lesson with explanations n examples. please..

Algebra, prove That J[i] is an euclidean ring

prove That J[i] is an euclidean ring

Leptokurtic-measure of central tendency, Leptokurtic a) A frequency di...

Leptokurtic a) A frequency distribution which is lepkurtic has normally a higher peak than that of the general distribution. The coefficient of kurtosis while determined will

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