Internal problem ID [4688]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}-\ln \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} x +\frac {c_{2}}{x}+\frac {x^{2} \left (3 \ln \left (x \right )-4\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 32
DSolve[y''[x]+1/x*y'[x]-1/x^2*y[x]==Log[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {4 x^2}{9}+\frac {1}{3} x^2 \log (x)+c_2 x+\frac {c_1}{x} \\ \end{align*}