77.1.46 problem 65 (page 109)

Internal problem ID [17936]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 65 (page 109)
Date solved : Tuesday, January 28, 2025 at 11:13:55 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 33

dsolve(diff(y(x),x)^2*y(x)+diff(y(x),x)*(x-y(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: 0.107 (sec). Leaf size: 47

DSolve[D[y[x],x]^2*y[x]+D[y[x],x]*(x-y[x])-x==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*}