Internal problem ID [14365]
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: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {t +4 y}{4 t +y}=0} \]
✓ Solution by Maple
Time used: 1.141 (sec). Leaf size: 36
dsolve(diff(y(t),t)=(t+4*y(t))/(4*t+y(t)),y(t), singsol=all)
\[ y \left (t \right ) = \left (\operatorname {RootOf}\left (\textit {\_Z}^{10} c_{1} t^{2}-\textit {\_Z}^{6}-6 \textit {\_Z}^{4}-12 \textit {\_Z}^{2}-8\right )^{2}+1\right ) t \]
✓ Solution by Mathematica
Time used: 5.494 (sec). Leaf size: 456
DSolve[y'[t]==(t+4*y[t])/(4*t+y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1}^4 t+\text {$\#$1}^3 \left (10 t^2+e^{2 c_1}\right )+\text {$\#$1}^2 \left (-10 t^3+3 e^{2 c_1} t\right )+\text {$\#$1} \left (5 t^4+3 e^{2 c_1} t^2\right )-t^5+e^{2 c_1} t^3\&,1\right ] \\ y(t)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1}^4 t+\text {$\#$1}^3 \left (10 t^2+e^{2 c_1}\right )+\text {$\#$1}^2 \left (-10 t^3+3 e^{2 c_1} t\right )+\text {$\#$1} \left (5 t^4+3 e^{2 c_1} t^2\right )-t^5+e^{2 c_1} t^3\&,2\right ] \\ y(t)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1}^4 t+\text {$\#$1}^3 \left (10 t^2+e^{2 c_1}\right )+\text {$\#$1}^2 \left (-10 t^3+3 e^{2 c_1} t\right )+\text {$\#$1} \left (5 t^4+3 e^{2 c_1} t^2\right )-t^5+e^{2 c_1} t^3\&,3\right ] \\ y(t)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1}^4 t+\text {$\#$1}^3 \left (10 t^2+e^{2 c_1}\right )+\text {$\#$1}^2 \left (-10 t^3+3 e^{2 c_1} t\right )+\text {$\#$1} \left (5 t^4+3 e^{2 c_1} t^2\right )-t^5+e^{2 c_1} t^3\&,4\right ] \\ y(t)\to \text {Root}\left [\text {$\#$1}^5-5 \text {$\#$1}^4 t+\text {$\#$1}^3 \left (10 t^2+e^{2 c_1}\right )+\text {$\#$1}^2 \left (-10 t^3+3 e^{2 c_1} t\right )+\text {$\#$1} \left (5 t^4+3 e^{2 c_1} t^2\right )-t^5+e^{2 c_1} t^3\&,5\right ] \\ \end{align*}