83.34.1 problem 1

Internal problem ID [19414]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (H) at page 118
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:38:49 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} n \,x^{3} y^{\prime \prime \prime }&=y-x y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 44

dsolve(n*x^3*diff(y(x),x$3)=(y(x)-x*diff(y(x),x)),y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} x +c_{2} x^{\frac {n +\sqrt {n \left (n -1\right )}}{n}}+c_3 \,x^{\frac {n -\sqrt {n \left (n -1\right )}}{n}} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 47

DSolve[n*x^3*D[y[x],{x,3}]==(y[x]-x*D[y[x],x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (c_1 x^{-\frac {\sqrt {(n-1) n}}{n}}+c_2 x^{\frac {\sqrt {(n-1) n}}{n}}+c_3\right ) \]