77.1.138 problem 165 (page 240)

Internal problem ID [18028]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 165 (page 240)
Date solved : Tuesday, January 28, 2025 at 11:22:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=x \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+2*y(x)=x*ln(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 22

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

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