40.4.24 problem 23 (d)

Internal problem ID [6664]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 23 (d)
Date solved : Monday, January 27, 2025 at 02:18:31 PM
CAS classification : [_Abel]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 109

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

\begin{align*} y &= -\frac {x \sqrt {{\mathrm e}^{-x^{2}} x^{2}+{\mathrm e}^{-x^{2}}+c_1}+{\mathrm e}^{-\frac {x^{2}}{2}}}{\sqrt {{\mathrm e}^{-x^{2}} x^{2}+{\mathrm e}^{-x^{2}}+c_1}} \\ y &= \frac {-x \sqrt {{\mathrm e}^{-x^{2}} x^{2}+{\mathrm e}^{-x^{2}}+c_1}+{\mathrm e}^{-\frac {x^{2}}{2}}}{\sqrt {{\mathrm e}^{-x^{2}} x^{2}+{\mathrm e}^{-x^{2}}+c_1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 10.052 (sec). Leaf size: 85

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

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