Mathematica DSolve diff. equation over a particular domain <p>I am looking for a way to solve the following differential equation:</p> <pre><code>DSolve[(1 - b*Abs[z])*f[z]/a == f''[z], f[z], z] </code></pre> <p>Therefore I tried to DSolve it distinguishing z>0 from z&lt;0 such as:</p> <pre><code>DSolve[(1 - b*z)*f[z]/a == f''[z], f[z], z&gt;0] </code></pre> <p>But I still does not work. Maybe adding a domain explicitly would help but I can't find a way to do so.</p> <p>Does anyone has any idea how do do such things?</p> <p>Thank you for your help and time</p>