Internal problem ID [3308]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }-3 y-\left (-y+x \right )^{2}=-3 x +3} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve(diff(y(x),x) = 3-3*x+3*y(x)+(x-y(x))^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-x} c_{1} x -c_{1} {\mathrm e}^{-x}-x +2}{c_{1} {\mathrm e}^{-x}-1} \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 25
DSolve[y'[x]==3(1-x+y[x])+(x-y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {1}{1+c_1 e^x}-2 y(x)\to x-2 \end{align*}