90.4.10 problem 11

Internal problem ID [25105]
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 59
Problem number : 11
Date solved : Thursday, October 02, 2025 at 11:50:19 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(z(t),t) = 2*t*(z(t)-t^2); 
dsolve(ode,z(t), singsol=all);
 

\[ z = t^{2}+1+{\mathrm e}^{t^{2}} c_1 \]

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 18

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

\begin{align*} z(t)&\to t^2+c_1 e^{t^2}+1 \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 14

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

\[ z{\left (t \right )} = C_{1} e^{t^{2}} + t^{2} + 1 \]