83.23.33 problem 32

Internal problem ID [19314]
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 : 32
Date solved : Tuesday, January 28, 2025 at 01:31:44 PM
CAS classification : [_rational]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.317 (sec). Leaf size: 76

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

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