77.1.111 problem 139 (page 201)

Internal problem ID [18001]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 139 (page 201)
Date solved : Tuesday, January 28, 2025 at 11:19:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 17

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

\[ y(x)\to x \left (x^2+c_2 x+c_1\right ) \]