Program Description: Purpose of problem is to find differential equation if general solution of the differential equation is y ( x ) = c 1 e 10 x + c 2 e 100 x . Summary introduction: Problem will use the characteristic equation of homogeneous second order differential equation a y ″ + b y ′ + c y = 0 is a r 2 + b r + c = 0 . If the roots are r 1 and r 2 of the characteristic equation are real and distinct, then the general solution of the differential equation is, y ( x ) = c 1 e r 1 x + c 2 e r 2 x ....... (1) If the roots are r 1 and r 2 of the characteristic equation are real and equal, then the general solution of the differential equation is, y ( x ) = ( c 1 + x c 2 ) e r 1 x ....... (2)

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Chapter 3.1, Problem 46P

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Program Description:Purpose of problem is to find differential equation if general solution of the differential equation is y(x)=c1e10x+c2e100x .

Summary introduction: Problem will use the characteristic equation of homogeneous second order differential equation ay″+by′+cy=0 is ar2+br+c=0 .

If the roots are r1 and r2 of the characteristic equation are real and distinct, then the general solution of the differential equation is,

y(x)=c1er1x+c2er2x ....... (1)

If the roots are r1 and r2 of the characteristic equation are real and equal, then the general solution of the differential equation is,

y(x)=(c1+xc2)er1x ....... (2)

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