Internal problem ID [10931]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 20(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (3 x +1\right ) y^{\prime }}{x}+\frac {y}{x}-3 x=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 52
dsolve((x^2-x)/x*diff(y(x),x$2)+(3*x+1)/x*diff(y(x),x)+y(x)/x=3*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} \left (2 \ln \left (x \right ) x^{2}+4 x -1\right )}{\left (x -1\right )^{3}}+\frac {c_{1} x^{2}}{\left (x -1\right )^{3}}+\frac {x^{3} \left (x^{2}-3 x +3\right )}{3 \left (x -1\right )^{3}} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 52
DSolve[(x^2-x)/x*y''[x]+(3*x+1)/x*y'[x]+y[x]/x==3*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x^2 (x ((x-3) x+3)-3 c_1)-6 c_2 x^2 \log (x)+3 c_2 (1-4 x)}{6 (x-1)^3} \\ \end{align*}