29.31.4 problem 903

Internal problem ID [5483]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 903
Date solved : Monday, January 27, 2025 at 11:27:13 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} x^{2} {y^{\prime }}^{2}+2 x \left (y+2 x \right ) y^{\prime }-4 a +y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 36

dsolve(x^2*diff(y(x),x)^2+2*x*(2*x+y(x))*diff(y(x),x)-4*a+y(x)^2 = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.309 (sec). Leaf size: 44

DSolve[x^2 (D[y[x],x])^2+2 x(2 x+y[x])D[y[x],x]-4 a+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-a+c_1 (-2 x+c_1)}{x} \\ y(x)\to -2 \sqrt {a} \\ y(x)\to 2 \sqrt {a} \\ \end{align*}