29.2.19 problem 44

Internal problem ID [4652]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 44
Date solved : Monday, January 27, 2025 at 09:29:29 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.189 (sec). Leaf size: 25

DSolve[D[y[x],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*}