83.26.17 problem 17

Internal problem ID [19341]
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 : 17
Date solved : Tuesday, January 28, 2025 at 01:34:36 PM
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: 0.003 (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)
 

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

✓ Solution by Mathematica

Time used: 0.034 (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]
 

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