Internal problem ID [11345]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first.
Article 62. Summary. Page 144
Problem number: Ex 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve((1-x^2)*diff(y(x),x$2)-1/x*diff(y(x),x)+x^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}}{2}+\sqrt {-1+x}\, \sqrt {1+x}\, c_{1} +c_{2} \]
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 30
DSolve[(1-x^2)*y''[x]-1/x*y'[x]+x^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{2}-c_1 \sqrt {1-x^2}+c_2 \]