77.1.109 problem 137 (page 198)

Internal problem ID [17999]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 137 (page 198)
Date solved : Tuesday, January 28, 2025 at 08:28:28 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }+x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 16

dsolve(x*diff(y(x),x$3)-diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 21

DSolve[x*D[y[x],{x,3}]-D[y[x],{x,2}]+x*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x+c_3 \cos (x)-c_2 \sin (x) \]