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Asked: 2026-05-22T00:57:58+00:00

Write y”[x] + ( [Epsilon] * Exp[x/3] * y[x] )==0. For [Epsilon]=0 Solve for

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Write 

                 y''[x] + ( [Epsilon] * Exp[x/3] * y[x] )==0.

For [Epsilon]=0

Solve for y[x] with initial conditions 

                            y[0]=y'[0]=1
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1 Answer

  1. Editorial Team
    eq = y''[x] + Epsilon*Exp[x/3]*y[x] == 0
soln = DSolve[eq, y[x], x]

    gives an answer, and then you can even do 

    Series[y[x] /. soln[[1]], {Epsilon, 0, 2}]

    which is ugly.

    To add initial conditions, you just add equations:

    soln2 = DSolve[{eq, y[0]==1, y'[0]==1}, y[x], x]//Simplify
Series[y[x] /. soln2[[1]], {Epsilon, 0, 2}]//Simplify

    (where I’ve added //Simplify to force Mathematica to put it into nice form.

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