Internal problem ID [11726]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page
124
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+y \left (1+x \right )=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([(x^2-x+1)*diff(y(x),x$2)-(x^2+x)*diff(y(x),x)+(x+1)*y(x)=0,x],singsol=all)
\[ y \left (x \right ) = c_{1} x +c_{2} {\mathrm e}^{x} \left (-1+x \right ) \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 19
DSolve[(x^2-x+1)*y''[x]-(x^2+x)*y'[x]+(x+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x+c_2 e^x (x-1) \]