29.31.29 problem 929

Internal problem ID [5508]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 929
Date solved : Monday, January 27, 2025 at 11:34:24 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.238 (sec). Leaf size: 66

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

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

✓ Solution by Mathematica

Time used: 0.913 (sec). Leaf size: 57

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

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