83.24.2 problem 2

Internal problem ID [19316]
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 (A) at page 81
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:34:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

\[ y \left (x \right ) = c_{2} x +\ln \left (x \right ) c_{1} x +2 \ln \left (x \right )+4 \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 20

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

\[ y(x)\to c_1 x+(2+c_2 x) \log (x)+4 \]