15.3.18 problem 18

Internal problem ID [2911]
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 : 18
Date solved : Monday, January 27, 2025 at 06:53:58 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (-4\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.140 (sec). Leaf size: 20

dsolve([(x-2*y(x)+3)+(1-x+2*y(x))*diff(y(x),x)=0,y(-4) = 2],y(x), singsol=all)
 

\[ y = \frac {7}{2}+\frac {x}{2}+4 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {5}{8}+\frac {x}{8}}}{8}\right ) \]

✓ Solution by Mathematica

Time used: 4.659 (sec). Leaf size: 28

DSolve[{(x-2*y[x]+3)+(1-x+2*y[x])*D[y[x],x]==0,{y[-4]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (8 W\left (\frac {1}{8} e^{\frac {x+5}{8}}\right )+x+7\right ) \]