I have a problem with solving the following differential equation: $(x^a u'(x))'=0$, where x and a are in $(0,1)$ and $[0,1)$, respectively.The derivative given in equation is with respect to $x$. I used Mathematica and got the following solution: $C_{2}+ (C_{1}/1-a)*x^(1-a)$. But I didn't get it's detail. Could you please share detail for this solution or help me in getting step by step solution from Mathematica?

All the best,

  • $\begingroup$ Welcome to the Mathematica Stack Exchange. Please include Mathematica code (not an image) so that forum participants can study the problem and help you further. You can copy directly from the input cell and paste in the Edit window, There is a { ... } icon to format it as code. $\endgroup$
    – Syed
    Commented Dec 18, 2022 at 5:25

1 Answer 1


eqn = D[x^a u'[x], x] == 0

(* a x^(-1 + a) u'[x] + x^a u''[x] == 0 *)

sol = DSolve[eqn, u, x][[1]]

(* {u -> Function[{x}, (x^(1 - a) C[1])/(1 - a) + C[2]]} *)

Verifying the solution

eqn /. sol

(* True *)

u[x] /. sol

(* (x^(1 - a) C[1])/(1 - a) + C[2] *)

Mathematica doesn't provide step-by-step solutions. However, it can be used to call WolframAlpha which does in some cases -- such as this

WolframAlpha["DSolve[a x^(a-1) u'[x] + x^a u''[x] == 0, u[x], x]"]

enter image description here


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.