90.7.9 problem 9

Internal problem ID [25163]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 99
Problem number : 9
Date solved : Thursday, October 02, 2025 at 11:55:53 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

With initial conditions

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

✓ Maple. Time used: 0.094 (sec). Leaf size: 5

ode:=diff(y(t),t) = 1+(t-y(t))^2; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = t \]

✓ Mathematica. Time used: 0.089 (sec). Leaf size: 6

ode=D[y[t],t]== 1+(t-y[t])^2; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-(t - y(t))**2 + Derivative(y(t), t) - 1,0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

ValueError : Couldnt solve for initial conditions