29.2.22 problem 47

Internal problem ID [4655]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 47
Date solved : Monday, January 27, 2025 at 09:29:36 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Riccati]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 34

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

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