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Chapter 8: Q5.7P (page 414)

Solve the following differential equations by the methods discussed above and compare computer solutions.

D2-5D+6y=0

Short Answer

Expert verified

The solution is y=c1e2x+c2e3x.

Step by step solution

01

Given information

A differential equation is given as D2-5D+6y=0.

02

Differential equation. 

A differential equation of the form (D-a)(D-b)y=0,a鈮�bhas general solution

y=c1eax+c2ebx.

03

Find the solution of given differential equation.

Suppose that D=ddx.

Then

Dy=dydxDy=y'D2y=ddxdydxd2ydx2=y''

Given differential equation is D2-5D+6y=0.

Auxiliary equation is-

D2-5D+6=0(D-2)(D-3)=0D=2D=3

These are unequal roots.

鈬�D=2,D=3

Differential equation becomes

鈬�(D-2)(D-3)y=0

These are separable equation with solution

y=c1e2xandy=c2e3x

The general solution will be given by y=c1e2x+c2e3x.

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Most popular questions from this chapter

Find the inverse Laplace transform of e-2PlP2in the following ways:

(a) Using L5 and L27 and the convolution integral of Section 10;

(b) Using L28.

Use L28 to find the Laplace transform of

f(t)={sin(t-蟺/2,t>蟺/20,t<蟺/2

Solve by use of Fourier series. Assume in each case that the right-hand side is a periodic function whose values are stated for one period.

y"+2y'+2y=|x|,-蟺<x<蟺.

Obtain L(te-atcosbt)

By using Laplace transforms, solve the following differential equations subject to the given initial conditions.

y"+4y'+4y=e-2t,yv=0,尉0=4
See all solutions

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