Internal problem ID [4355]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (1+x \right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x -1 \end {align*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 20
dsolve([x*(x+1)*diff(y(x),x$2)-(x-1)*diff(y(x),x)+y(x)=0,x-1],y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x -1\right )+c_{2} \left (-4+\left (x -1\right ) \ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 23
DSolve[x*(x+1)*y''[x]-(x-1)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x-1)+c_2 ((x-1) \log (x)-4) \\ \end{align*}