39.4.6 problem Problem 12.14

Internal problem ID [6540]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page 109
Problem number : Problem 12.14
Date solved : Monday, January 27, 2025 at 02:11:57 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

\[ y = c_1 x +\frac {c_2}{x}+\frac {x^{2} \left (3 \ln \left (x \right )-4\right )}{9} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 32

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

\[ y(x)\to -\frac {4 x^2}{9}+\frac {1}{3} x^2 \log (x)+c_2 x+\frac {c_1}{x} \]