29.3.10 problem 64

Internal problem ID [4672]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 64
Date solved : Monday, January 27, 2025 at 09:30:58 AM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 56

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

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

✓ Solution by Mathematica

Time used: 0.256 (sec). Leaf size: 40

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

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