74.7.53 problem 58

Internal problem ID [16130]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 58
Date solved : Tuesday, January 28, 2025 at 08:50:23 AM
CAS classification : [_dAlembert]

\begin{align*} y&=-y^{\prime } t +\frac {{y^{\prime }}^{5}}{5} \end{align*}

✓ Solution by Maple

Time used: 0.122 (sec). Leaf size: 32

dsolve(y(t)=-t*diff(y(t),t)+1/5*diff(y(t),t)^5,y(t), singsol=all)
 

\[ \left [t \left (\textit {\_T} \right ) = \frac {\textit {\_T}^{{9}/{2}}+9 c_{1}}{9 \sqrt {\textit {\_T}}}, y \left (\textit {\_T} \right ) = \frac {4 \textit {\_T}^{5}}{45}-\sqrt {\textit {\_T}}\, c_{1}\right ] \]

✓ Solution by Mathematica

Time used: 1.991 (sec). Leaf size: 2076

DSolve[y[t]==-t*D[y[t],t]+1/5*D[y[t],t]^5,y[t],t,IncludeSingularSolutions -> True]
 

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