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Chapter 8: Q5.5P (page 414)

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

D2-2D+1y=0

Short Answer

Expert verified

The solution is y=(Ax+B)ex.

Step by step solution

01

Given information

A differential equation is given as D2-2D+1y=0.

02

Differential equation. 

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

y=(Ax+B)eax.

03

Calculate the solution of given differential equation.

Suppose that D=ddx.

Then

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

Given differential equation is D2-2D+1y=0.

Above equation becomes,

(D-1)(D-1)y=0(D-1)y=0and(D-1)y=0

The general solution will be given by y=(Ax+B)ex.

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Most popular questions from this chapter

Using (3.9), find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after (3.9), and Example 1.

y'+ytanhx=2ex

Solve Example 4 using the general solution y=asinhx+bcoshx.

Solve the differential equation yy2+2xy'-y=0by changing from variables role="math" localid="1655272385100" y,xto r,x where y2=r2; then yy'=n'-x.

(1+y2)dx+xydy=0,y=0when x=5.

Using (3.9), find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after (3.9), and Example 1.

2xy+y=2x5/2
See all solutions

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