80.2.3 problem 4 (c)

Internal problem ID [18542]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 24. Problems at page 62
Problem number : 4 (c)
Date solved : Tuesday, January 28, 2025 at 11:55:15 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (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: 0.043 (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*}