80.6.5 problem 8 (eq 68)

Internal problem ID [18569]
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 33. Problems at page 91
Problem number : 8 (eq 68)
Date solved : Tuesday, January 28, 2025 at 12:00:34 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

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

\[ y \left (x \right ) = \frac {\tan \left (\frac {\sqrt {b a}\, \left (x^{2}+2 c_{1} \right )}{2}\right ) \sqrt {b a}}{a} \]

✓ Solution by Mathematica

Time used: 8.114 (sec). Leaf size: 75

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

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