Internal problem ID [5827]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 2. Linear homogeneous equations. Section 2.3.4 problems. page 104
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 y^{\prime \prime } x +\left (x -2\right ) y^{\prime }-y=x^{2}-1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(2*x*diff(y(x),x$2)+(x-2)*diff(y(x),x)-y(x)=x^2-1,y(x), singsol=all)
\[ y \left (x \right ) = \left (x -2\right ) c_{2} +c_{1} {\mathrm e}^{-\frac {x}{2}}+x^{2}+1 \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 30
DSolve[2*x*y''[x]+(x-2)*y'[x]-y[x]==x^2-1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2-4 x+c_1 e^{-x/2}+2 c_2 (x-2)+9 \]