62.32.7 problem Ex 7

Internal problem ID [12984]
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
Date solved : Tuesday, January 28, 2025 at 04:46:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

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)
 

\[ y = c_{2} x^{3}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 1.284 (sec). Leaf size: 19

DSolve[(2*x^3-1)*D[y[x],{x,2}]-6*x^2*D[y[x],x]+6*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x-c_2 \left (x^3+1\right ) \]