Internal problem ID [6704]
Book: Second order enumerated odes
Section: section 2
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y-2 x^{3}+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 26
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+3*y(x)=2*x^3-x^2,y(x), singsol=all)
\[ y \relax (x ) = \left (\ln \relax (x ) x^{2}-\frac {x^{2}}{2}+x +\frac {c_{1} x^{2}}{2}+c_{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 27
DSolve[x^2*y''[x]-3*x*y'[x]+3*y[x]==2*x^3-x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (x^2 \log (x)+\left (-\frac {1}{2}+c_2\right ) x^2+x+c_1\right ) \\ \end{align*}