Internal problem ID [14342]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 59 (ii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y+\left (2 t +2 y\right ) y^{\prime }=-\frac {9 t}{5}} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 53
dsolve((18/10*t+2*y(t))+(2*t+2*y(t))*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {-10 c_{1} t -\sqrt {10 c_{1}^{2} t^{2}+10}}{10 c_{1}} \\ y \left (t \right ) &= \frac {-10 c_{1} t +\sqrt {10 c_{1}^{2} t^{2}+10}}{10 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.549 (sec). Leaf size: 101
DSolve[(18/10*t+2*y[t])+(2*t+2*y[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -t-\frac {\sqrt {t^2+e^{20 c_1}}}{\sqrt {10}} \\ y(t)\to -t+\frac {\sqrt {t^2+e^{20 c_1}}}{\sqrt {10}} \\ y(t)\to -\frac {\sqrt {t^2}}{\sqrt {10}}-t \\ y(t)\to \frac {\sqrt {t^2}}{\sqrt {10}}-t \\ \end{align*}