Internal problem ID [14360]
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: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]
\[ \boxed {\left (y-3 t \right ) y^{\prime }=-2 t} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 47
dsolve(( 2*t )+( y(t)-3*t )*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {2 c_{1} t -\sqrt {-4 c_{1} t +1}+1}{2 c_{1}} \\ y \left (t \right ) &= \frac {2 c_{1} t +1+\sqrt {-4 c_{1} t +1}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.268 (sec). Leaf size: 76
DSolve[( 2*t )+( y[t]-3*t )*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} \left (2 t-e^{\frac {c_1}{2}} \sqrt {-4 t+e^{c_1}}+e^{c_1}\right ) \\ y(t)\to \frac {1}{2} \left (2 t+e^{\frac {c_1}{2}} \sqrt {-4 t+e^{c_1}}+e^{c_1}\right ) \\ \end{align*}