Internal problem ID [14428]
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.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-y^{\prime } t -3 {y^{\prime }}^{4}=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 68
dsolve(y(t)=t*diff(y(t),t)+3*diff(y(t),t)^4,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= -\frac {18^{\frac {1}{3}} \left (-t \right )^{\frac {4}{3}}}{8} \\ y \left (t \right ) &= \frac {18^{\frac {1}{3}} \left (-t \right )^{\frac {4}{3}} \left (1+i \sqrt {3}\right )}{16} \\ y \left (t \right ) &= -\frac {18^{\frac {1}{3}} \left (-t \right )^{\frac {4}{3}} \left (i \sqrt {3}-1\right )}{16} \\ y \left (t \right ) &= c_{1} \left (3 c_{1}^{3}+t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 81
DSolve[y[t]==t*y'[t]+3*y'[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*}