60.1.468 problem 471

Internal problem ID [10482]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 471
Date solved : Monday, January 27, 2025 at 07:55:04 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

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

\begin{align*} y &= \sqrt {-x^{2}+c_{1}} \\ y &= -\sqrt {-x^{2}+c_{1}} \\ y &= x +c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.125 (sec). Leaf size: 47

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

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