72.8.30 problem 45

Internal problem ID [14723]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 45
Date solved : Monday, March 31, 2025 at 12:55:31 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=t^{2} y+1+y+t^{2} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = -1+{\mathrm e}^{\frac {t \left (t^{2}+3\right )}{3}} c_1 \]

✓ Mathematica. Time used: 0.299 (sec). Leaf size: 26

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

\begin{align*} y(t)\to -1+c_1 e^{\frac {t^3}{3}+t} \\ y(t)\to -1 \\ \end{align*}

✓ Sympy. Time used: 0.301 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = C_{1} e^{t \left (\frac {t^{2}}{3} + 1\right )} - 1 \]