Internal problem ID [11715]
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
113
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime } x +x^{2} y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.641 (sec). Leaf size: 5
dsolve([diff(y(x),x$2)+x*diff(y(x),x)+x^2*y(x)=0,y(1) = 0, D(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 6
DSolve[{y''[x]+x*y'[x]+x^2*y[x]==0,{y[1]==0,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 0 \]