15.3.15 problem 15

Internal problem ID [2908]
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 : 15
Date solved : Monday, January 27, 2025 at 06:52:59 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (3\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.156 (sec). Leaf size: 20

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

\[ y = \frac {7}{3}-\frac {2 x}{3}+3 \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {5}{9}-\frac {x}{9}}}{9}\right ) \]

✓ Solution by Mathematica

Time used: 4.623 (sec). Leaf size: 32

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

\[ y(x)\to \frac {1}{3} \left (9 W\left (\frac {2}{9} e^{\frac {5}{9}-\frac {x}{9}}\right )-2 x+7\right ) \]