Internal problem ID [13059]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _Riccati]
\[ \boxed {y^{\prime }-\left (y-x \right )^{2}=1} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{4}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 18
dsolve([diff(y(x),x)=1+(y(x)-x)^2,y(0) = 1/4],y(x), singsol=all)
\[ y = \frac {x^{2}-4 x -1}{x -4} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 19
DSolve[{y'[x]==1+(y[x]-x)^2,{y[0]==1/4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2-4 x-1}{x-4} \]