77.1.139 problem 166 (page 240)

Internal problem ID [18029]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 166 (page 240)
Date solved : Tuesday, January 28, 2025 at 11:23:00 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve(x^2*diff(y(x),x$2)-2*y(x)=x^2+1/x,y(x), singsol=all)
 

\[ y = \frac {3 x^{3} \ln \left (x \right )+9 c_{2} x^{3}-3 \ln \left (x \right )+9 c_{1} -1}{9 x} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 37

DSolve[x^2*D[y[x],{x,2}]-2*y[x]==x^2+1/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 \left (x^3-1\right ) \log (x)+(-1+9 c_2) x^3-1+9 c_1}{9 x} \]