Internal problem ID [2798]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 43.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\left (x -y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve(diff(y(x),x) = (x-y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x \,{\mathrm e}^{2 x} c_{1}-c_{1} {\mathrm e}^{2 x}-x -1}{-1+c_{1} {\mathrm e}^{2 x}} \]
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 29
DSolve[y'[x]==(x-y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {1}{\frac {1}{2}+c_1 e^{2 x}}-1 \\ y(x)\to x-1 \\ \end{align*}