15.3.14 problem 14

Internal problem ID [2907]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 14
Date solved : Monday, January 27, 2025 at 06:52:57 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.135 (sec). Leaf size: 20

dsolve([(x+y(x)+4)=(2*x+2*y(x)-1)*diff(y(x),x),y(0) = 0],y(x), singsol=all)
 

\[ y = -x -\frac {3 \operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{-x -\frac {2}{3}}}{3}\right )}{2}-1 \]

✓ Solution by Mathematica

Time used: 3.206 (sec). Leaf size: 28

DSolve[{(x+y[x]+4)==(2*x+2*y[x]-1)*D[y[x],x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {3}{2} W\left (-\frac {2}{3} e^{-x-\frac {2}{3}}\right )-x-1 \]