15.3.19 problem 19

Internal problem ID [2912]
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 : 19
Date solved : Monday, January 27, 2025 at 06:54:00 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (-\frac {1}{6}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.179 (sec). Leaf size: 21

dsolve([(2*x+y(x))+(4*x+2*y(x)+1)*diff(y(x),x)=0,y(-1/6) = 0],y(x), singsol=all)
 

\[ y = -\frac {\operatorname {LambertW}\left (-1, -2 \,{\mathrm e}^{-\frac {7}{2}-9 x}\right )}{6}-\frac {2}{3}-2 x \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{(2*x+y[x])+(4*x+2*y[x]+1)*D[y[x],x]==0,{y[-1/6]==0}},y[x],x,IncludeSingularSolutions -> True]
 

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