2.56 problem Problem 20(c)

Internal problem ID [10929]

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: 0.0 (sec). Leaf size: 28

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)
 

\[ y \left (x \right ) = \frac {c_{1}}{x}+\frac {c_{2} \left (x^{2}+2 \ln \left (x +1\right )-2 x \right )}{x} \]

Solution by Mathematica

Time used: 0.015 (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]
 

\begin{align*} y(x)\to \frac {c_2 (x-3) (x+1)+2 c_2 \log (x+1)+2 c_1}{2 x} \\ \end{align*}