29.7.1 problem 176

Internal problem ID [4776]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 176
Date solved : Monday, January 27, 2025 at 09:37:21 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x y^{\prime }&=x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(x*diff(y(x),x) = x^3+(2*x^2+1)*y(x)+x*y(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {x \left (x^{2}+2 c_{1} +2\right )}{x^{2}+2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 34

DSolve[x D[y[x],x]==x^3+(1+2 x^2)y[x]+x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x \left (x^2+2+2 c_1\right )}{x^2+2 c_1} \\ y(x)\to -x \\ \end{align*}