Internal problem ID [11729]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 17, Reduction of order. Exercises page 162
Problem number: 17.2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{x} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve([(x-1)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,exp(x)],y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x +c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 17
DSolve[(x-1)*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^x-c_2 x \]