13.3.20 problem 23

Internal problem ID [2337]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.4. Page 24
Problem number : 23
Date solved : Monday, January 27, 2025 at 05:47:53 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (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 &= -\frac {t}{2}+\frac {1}{4}-\frac {\sqrt {28 c_1 -28 t +1}}{4} \\ y &= -\frac {t}{2}+\frac {1}{4}+\frac {\sqrt {28 c_1 -28 t +1}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 55

DSolve[(t+2*y[t]+3)+(2*t+4*y[t]-1)*D[y[t],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*}