83.23.31 problem 31 (a)

Internal problem ID [19312]
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 : 31 (a)
Date solved : Tuesday, January 28, 2025 at 01:31:41 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y \left (x \right ) = \frac {a +x}{a x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.613 (sec). Leaf size: 34

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

\begin{align*} y(x)\to \frac {a+x}{a^2+a x+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to \frac {1}{a} \\ \end{align*}