Internal problem ID [10295]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page
129
Problem number: Ex 8.
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 }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y-x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-2*x*(1+x)*diff(y(x),x)+2*(1+x)*y(x)=x^3,y(x), singsol=all)
\[ y \relax (x ) = x c_{2}+x \,{\mathrm e}^{2 x} c_{1}-\frac {x^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 28
DSolve[x^2*y''[x]-2*x*(1+x)*y'[x]+2*(1+x)*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{4} x \left (2 x-2 c_2 e^{2 x}+1-4 c_1\right ) \\ \end{align*}