77.1.103 problem Example 1 (page 195)

Internal problem ID [17993]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : Example 1 (page 195)
Date solved : Tuesday, January 28, 2025 at 11:19:34 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 x y^{\prime }-12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 16

dsolve(2*x^3*diff(y(x),x$3)-6*x^2*diff(y(x),x$2)+12*x*diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
 

\[ y = x \left (c_{1} x^{2}+c_{2} x +c_{3} \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 19

DSolve[2*x^3*D[y[x],{x,3}]-6*x^2*D[y[x],{x,2}]+12*x*D[y[x],x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (x (c_3 x+c_2)+c_1) \]