29.6.18 problem 164

Internal problem ID [4764]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 164
Date solved : Monday, January 27, 2025 at 09:36:44 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 12

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

\[ y(x)\to x \tan (x+c_1) \]