47.5.5 problem 5

Internal problem ID [7494]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.3.4 problems. page 104
Problem number : 5
Date solved : Monday, January 27, 2025 at 03:02:18 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x \left (1+x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y&=x +\frac {1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 42

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

\[ y = \frac {2 \ln \left (x \right ) x^{2}+4 c_{2} x^{2}+4 \ln \left (x \right ) x +8 c_{2} x +4 c_{1} +4 c_{2} +6 x +5}{4 x} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 37

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

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