68.1.48 problem 55

Internal problem ID [17115]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 55
Date solved : Thursday, October 02, 2025 at 01:43:23 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 17

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

\[ y = x^{4}-\frac {1}{2} x^{2}+1+2 x \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to x^4-\frac {x^2}{2}+2 x+1 \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = x^{4} - \frac {x^{2}}{2} + 2 x + 1 \]