Internal problem ID [3307]
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]
\[ \boxed {y^{\prime }-\left (-y+x \right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x) = (x-y(x))^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \,{\mathrm e}^{-2 x} c_{1} +{\mathrm e}^{-2 x} c_{1} -x +1}{{\mathrm e}^{-2 x} c_{1} -1} \]
✓ Solution by Mathematica
Time used: 0.126 (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*}