Internal problem ID [14412]
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: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]
\[ \boxed {\left (-4 y+t \right ) y^{\prime }=-3 t} \]
✓ Solution by Maple
Time used: 1.11 (sec). Leaf size: 49
dsolve(3*t+(t-4*y(t))*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \frac {t \left (\operatorname {RootOf}\left (\textit {\_Z}^{49} c_{1} t^{7}-21 \textit {\_Z}^{42} c_{1} t^{7}+147 \textit {\_Z}^{35} c_{1} t^{7}-343 \textit {\_Z}^{28} c_{1} t^{7}-64\right )^{7}-3\right )}{4} \]
✓ Solution by Mathematica
Time used: 3.627 (sec). Leaf size: 477
DSolve[3*t+(t-4*y[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,1\right ] \\ y(t)\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,2\right ] \\ y(t)\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,3\right ] \\ y(t)\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,4\right ] \\ y(t)\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,5\right ] \\ y(t)\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,6\right ] \\ y(t)\to \text {Root}\left [256 \text {$\#$1}^7-672 \text {$\#$1}^5 t^2-112 \text {$\#$1}^4 t^3+609 \text {$\#$1}^3 t^4+189 \text {$\#$1}^2 t^5-189 \text {$\#$1} t^6-81 t^7+e^{7 c_1}\&,7\right ] \\ \end{align*}