35.7.25 problem 30

Internal problem ID [6207]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 30
Date solved : Monday, January 27, 2025 at 01:47:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x \left (1+x \right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=x -1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve([x*(x+1)*diff(y(x),x$2)-(x-1)*diff(y(x),x)+y(x)=0,x-1],singsol=all)
 

\[ y = \left (x -1\right ) c_{2} \ln \left (x \right )-4 c_{2} +c_{1} \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 23

DSolve[x*(x+1)*D[y[x],{x,2}]-(x-1)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 (x-1)+c_2 ((x-1) \log (x)-4) \]