29.2.21 problem 46

Internal problem ID [4654]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 46
Date solved : Monday, January 27, 2025 at 09:29:35 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Riccati]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

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

\[ y \left (x \right ) = \frac {c_{1} x^{2}+x^{3}-1}{x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.145 (sec). Leaf size: 24

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

\begin{align*} y(x)\to x^2+\frac {1}{-x+c_1} \\ y(x)\to x^2 \\ \end{align*}