83.28.4 problem 4

Internal problem ID [19369]
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 (B) at page 106
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:35:38 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} x^{3} y^{\prime \prime \prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x^3*diff(y(x),x$3)=1,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\ln \left (x \right )}{2}+\frac {c_{1} x^{2}}{2}+c_{2} x +c_3 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 23

DSolve[x^3*D[y[x],{x,3}]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\log (x)}{2}+x (c_3 x+c_2)+c_1 \]