29.30.38 problem 898

Internal problem ID [5478]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 898
Date solved : Monday, January 27, 2025 at 11:26:55 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x +y \left (y+1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.126 (sec). Leaf size: 22

dsolve(x^2*diff(y(x),x)^2-2*x*diff(y(x),x)*y(x)-x+y(x)*(1+y(x)) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 55

DSolve[x^2 (D[y[x],x])^2-2 x y[x] D[y[x],x]-x+y[x](1+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x+\frac {c_1{}^2 x}{4}-i c_1 \sqrt {x}-1 \\ y(x)\to x+\frac {c_1{}^2 x}{4}+i c_1 \sqrt {x}-1 \\ \end{align*}