69.1.74 problem 118

Internal problem ID [14227]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 118
Date solved : Tuesday, January 28, 2025 at 06:22:39 AM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} x y^{\prime \prime \prime }&=2 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve(x*diff(y(x),x$3)=2,y(x), singsol=all)
 

\[ y = \ln \left (x \right ) x^{2}+\frac {\left (c_{1} -3\right ) x^{2}}{2}+c_{2} x +c_{3} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 28

DSolve[x*D[y[x],{x,3}]==2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \log (x)+\left (-\frac {3}{2}+c_3\right ) x^2+c_2 x+c_1 \]