79.1.1 problem 1 (i)

Internal problem ID [18409]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 1 (i)
Date solved : Thursday, March 13, 2025 at 11:55:48 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=3 t^{2}+4 t \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 14

ode:=diff(x(t),t) = 3*t^2+4*t; 
ic:=x(1) = 0; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = t^{3}+2 t^{2}-3 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 15

ode=D[x[t],t]==3*t^2+4*t; 
ic={x[1]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to t^3+2 t^2-3 \]

✓ Sympy. Time used: 0.142 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-3*t**2 - 4*t + Derivative(x(t), t),0) 
ics = {x(1): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = t^{3} + 2 t^{2} - 3 \]