83.26.8 problem 8

Internal problem ID [19332]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 01:34:24 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 27

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

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