74.8.26 problem 26

Internal problem ID [16162]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 08:53:14 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.173 (sec). Leaf size: 66

dsolve(y(t)=t*diff(y(t),t)+3*diff(y(t),t)^4,y(t), singsol=all)
 

\begin{align*} y &= -\frac {18^{{1}/{3}} \left (-t \right )^{{4}/{3}}}{8} \\ y &= \frac {18^{{1}/{3}} \left (-t \right )^{{4}/{3}} \left (1+i \sqrt {3}\right )}{16} \\ y &= -\frac {18^{{1}/{3}} \left (-t \right )^{{4}/{3}} \left (i \sqrt {3}-1\right )}{16} \\ y &= c_{1} \left (3 c_{1}^{3}+t \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 81

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

\begin{align*} y(t)\to c_1 \left (t+3 c_1{}^3\right ) \\ y(t)\to -\frac {1}{4} \left (-\frac {3}{2}\right )^{2/3} t^{4/3} \\ y(t)\to -\frac {1}{4} \left (\frac {3}{2}\right )^{2/3} t^{4/3} \\ y(t)\to \frac {1}{4} \sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} t^{4/3} \\ \end{align*}