77.1.137 problem 164 (page 240)

Internal problem ID [18027]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 164 (page 240)
Date solved : Tuesday, January 28, 2025 at 11:22:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 16

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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