29.30.10 problem 869

Internal problem ID [5450]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 869
Date solved : Monday, January 27, 2025 at 11:24:16 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x {y^{\prime }}^{2}-3 y^{\prime } y+9 x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.145 (sec). Leaf size: 51

dsolve(x*diff(y(x),x)^2-3*y(x)*diff(y(x),x)+9*x^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -2 x^{{3}/{2}} \\ y \left (x \right ) &= 2 x^{{3}/{2}} \\ y \left (x \right ) &= \frac {4 x^{3}+c_{1}^{2}}{2 c_{1}} \\ y \left (x \right ) &= \frac {x^{3} c_{1}^{2}+4}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.302 (sec). Leaf size: 79

DSolve[x (D[y[x],x])^2-3 y[x] D[y[x],x]+9 x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right ) \\ y(x)\to \frac {1}{2} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right ) \\ y(x)\to -2 x^{3/2} \\ y(x)\to 2 x^{3/2} \\ \end{align*}