Internal problem ID [1687]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y+\left (2 t +4 y-1\right ) y^{\prime }=-t -3} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
dsolve((t+2*y(t)+3)+(2*t+4*y(t)-1)*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= -\frac {t}{2}+\frac {1}{4}-\frac {\sqrt {28 c_{1} -28 t +1}}{4} \\ y \left (t \right ) &= -\frac {t}{2}+\frac {1}{4}+\frac {\sqrt {28 c_{1} -28 t +1}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 55
DSolve[(t+2*y[t]+3)+(2*t+4*y[t]-1)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} \left (-2 t-\sqrt {-28 t+1+16 c_1}+1\right ) \\ y(t)\to \frac {1}{4} \left (-2 t+\sqrt {-28 t+1+16 c_1}+1\right ) \\ \end{align*}