74.11.11 problem 23

Internal problem ID [16261]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 08:59:06 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

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

dsolve(diff(y(t),t$2)=3*t^4-2*t,y(t), singsol=all)
 

\[ y = \frac {1}{10} t^{6}-\frac {1}{3} t^{3}+\frac {5}{18}+c_{1} t +c_{2} \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 26

DSolve[D[y[t],{t,2}]==3*t^4-2*t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t^6}{10}-\frac {t^3}{3}+c_2 t+c_1 \]