Variable coefficient Differential Equation - Mathematica Stack Exchange most recent 30 from mathematica.stackexchange.com 2019-09-20T17:48:06Z https://mathematica.stackexchange.com/feeds/question/111047 https://creativecommons.org/licenses/by-sa/4.0/rdf https://mathematica.stackexchange.com/q/111047 1 Variable coefficient Differential Equation Asim Aziz https://mathematica.stackexchange.com/users/38901 2016-03-25T14:11:23Z 2016-03-25T16:31:28Z <p>Can anyone help with the following differential equation. The errors i am getting are also given.</p> <pre><code>DSolve[{x y''[x] - h*x y'[x] + y'[x] == 0, y == 0, y == 1}, y[x], x] </code></pre> <blockquote> <p>During evaluation of In:= Solve::incnst: Inconsistent or redundant transcendental equation. After reduction, the bad equation is <code>-C == 0.</code> >></p> <p>During evaluation of In:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >></p> <p>During evaluation of In:= DSolve::bvnul: For some branches of the general solution, the given boundary conditions lead to an empty solution. >></p> </blockquote> <pre><code>Out= {} </code></pre> https://mathematica.stackexchange.com/questions/111047/-/111049#111049 3 Answer by bbgodfrey for Variable coefficient Differential Equation bbgodfrey https://mathematica.stackexchange.com/users/1063 2016-03-25T14:32:01Z 2016-03-25T14:32:01Z <p><code>y == 0</code> is at fault here. Omit it to obtain</p> <pre><code>DSolve[{x y''[x] - h*x y'[x] + y'[x] == 0, y == 1}, y[x], x][[1, 1]] (* y[x] -&gt; 1 - C ExpIntegralEi[h] + C ExpIntegralEi[h x] *) </code></pre> <p>However, <code>ExpIntegralEi[h x]</code> evaluates to Infinity at <code>x = 0</code>. Thus, <code>y == 0</code> has no solution.</p> <pre><code>y[x] /. % /. x -&gt; 0 (* 1 + C (-∞) - C ExpIntegralEi[h] *) </code></pre>