Internal problem ID [10294]
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 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((2*x^3-1)*diff(y(x),x$2)-6*x^2*diff(y(x),x)+6*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \left (x^{3}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.843 (sec). Leaf size: 19
DSolve[(2*x^3-1)*y''[x]-6*x^2*y'[x]+6*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-c_2 \left (x^3+1\right ) \\ \end{align*}