73.5.4 problem 6.2

Internal problem ID [15115]
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
Date solved : Tuesday, January 28, 2025 at 07:33:25 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=1+\left (y-x \right )^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{4}} \end{align*}

✓ Solution by Maple

Time used: 0.210 (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: 0.160 (sec). Leaf size: 19

DSolve[{D[y[x],x]==1+(y[x]-x)^2,{y[0]==1/4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2-4 x-1}{x-4} \]