Internal problem ID [5321]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
\[ \boxed {y^{\prime }+x \left (x +y\right )-x^{3} \left (x +y\right )^{3}=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 66
dsolve(diff(y(x),x)+x*(x+y(x))=x^3*(x+y(x))^3-1,y(x), singsol=all)
\begin{align*} y = -\frac {{\mathrm e}^{-\frac {x^{2}}{2}}}{\sqrt {c_{1} +\left (x^{2}+1\right ) {\mathrm e}^{-x^{2}}}}-x y = \frac {{\mathrm e}^{-\frac {x^{2}}{2}}}{\sqrt {c_{1} +\left (x^{2}+1\right ) {\mathrm e}^{-x^{2}}}}-x \end{align*}
✓ Solution by Mathematica
Time used: 10.062 (sec). Leaf size: 85
DSolve[y'[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*}