Internal problem ID [12277]
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(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x +1}-\frac {\left (x +2\right ) y}{x^{2} \left (x +1\right )}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+diff(y(x),x)/(1+x)-(2+x)/(x^2*(1+x))*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 \ln \left (1+x \right ) c_{2} +\left (x^{2}-2 x \right ) c_{2} +c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 34
DSolve[y''[x]+y'[x]/(1+x)-(2+x)/(x^2*(1+x))*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \left (x^2-2 x+2 \log (x+1)-3\right )+2 c_1}{2 x} \]