2.19 problem 44

Internal problem ID [2799]

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]

Solve \begin {gather*} \boxed {y^{\prime }-3+3 x -3 y-\left (x -y\right )^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.012 (sec). Leaf size: 28

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

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

Solution by Mathematica

Time used: 0.17 (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*}