83.23.30 problem 30

Internal problem ID [19311]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 01:30:48 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Timed out