74.1.48 problem 55

Internal problem ID [15828]
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 : Tuesday, January 28, 2025 at 08:08:25 AM
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*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 20

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

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