29.6.21 problem 167

Internal problem ID [4767]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 167
Date solved : Monday, January 27, 2025 at 09:37:01 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x y^{\prime }&=a \,x^{2}+y+b y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 19.208 (sec). Leaf size: 33

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

\[ y(x)\to \frac {\sqrt {a} x \tan \left (\sqrt {a} \sqrt {b} (x+c_1)\right )}{\sqrt {b}} \]