83.23.32 problem 31 (b)

Internal problem ID [19313]
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 (b)
Date solved : Tuesday, January 28, 2025 at 01:31:43 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 24

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

\begin{align*} y(x)\to \frac {b+c_1 x}{b x+1} \\ y(x)\to b \\ \end{align*}