76.3.7 problem 7

Internal problem ID [17378]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 10:03:38 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {t -y}{2 t +5 y} \end{align*}

✓ Solution by Maple

Time used: 1.937 (sec). Leaf size: 57

dsolve(diff(y(t),t)=(t-y(t))/(2*t+5*y(t)),y(t), singsol=all)
 

\[ -\frac {\ln \left (\frac {-t^{2}+3 t y+5 y^{2}}{t^{2}}\right )}{2}+\frac {\sqrt {29}\, \operatorname {arctanh}\left (\frac {\left (10 y+3 t \right ) \sqrt {29}}{29 t}\right )}{29}-\ln \left (t \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 44

DSolve[D[y[t],t]==(t-y[t])/(2*t+5*y[t]),y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(t)}{t}}\frac {5 K[1]+2}{5 K[1]^2+3 K[1]-1}dK[1]=-\log (t)+c_1,y(t)\right ] \]