90.5.1 problem 1

Internal problem ID [25120]
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 71
Problem number : 1
Date solved : Thursday, October 02, 2025 at 11:50:44 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} t^{2} y^{\prime }&=y^{2}+y t +t^{2} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 13

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

\[ y = \tan \left (\ln \left (t \right )+\frac {\pi }{4}\right ) t \]

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 16

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

\begin{align*} y(t)&\to t \tan \left (\log (t)+\frac {\pi }{4}\right ) \end{align*}

✓ Sympy. Time used: 0.178 (sec). Leaf size: 26

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

\[ y{\left (t \right )} = \frac {t \left (i e^{2 i \log {\left (t \right )}} - 1\right )}{- e^{2 i \log {\left (t \right )}} + i} \]