75.19.8 problem 625

Internal problem ID [17124]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 625
Date solved : Tuesday, January 28, 2025 at 09:53:39 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 24

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

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