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Chapter 6: Q8E (page 332)

Find a general solution for the differential equation with x as the independent variable:

2y'''+5y''鈭�13y'+7y=0

Short Answer

Expert verified

The general solution for the differential equation with x as the independent variable is y(x)=c1ex+c2xex+c3e鈭�7x

Step by step solution

01

Auxiliary equation:

Considering the equation

y'''+5y''鈭�13y'+7y=0

The associated auxiliary equation is r3+5r2鈭�13r'+7=(r鈭�1)2(r+7)=0which has a double solution and r = -7 as a simple solution.

02

General solution:

The general solution to the equation is y(x)=c1ex+c2xex+c3e鈭�7x

Hence the final solution is y(x)=c1ex+c2xex+c3e鈭�7x

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Most popular questions from this chapter

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