29.33.15 problem 977

Internal problem ID [5554]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 977
Date solved : Monday, January 27, 2025 at 11:46:25 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Solution by Maple

Time used: 0.248 (sec). Leaf size: 57

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

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

✓ Solution by Mathematica

Time used: 0.551 (sec). Leaf size: 61

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

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