29.30.11 problem 870

Internal problem ID [5451]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 870
Date solved : Monday, January 27, 2025 at 11:24:23 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 26

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

\begin{align*} y(x)\to c_1 x^3 \\ y(x)\to 2 x+c_1 \\ y(x)\to 0 \\ \end{align*}