15.3.12 problem 12

Internal problem ID [2905]
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 : 12
Date solved : Monday, January 27, 2025 at 06:28:28 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.219 (sec). Leaf size: 20

dsolve([3*(2*x-y(x)+2)+(2*x-y(x)+5)*diff(y(x),x)=0,y(-1) = 1],y(x), singsol=all)
 

\[ y = \frac {16}{5}-\frac {9 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {25 x}{9}+\frac {26}{9}}}{9}\right )}{5}+2 x \]

✓ Solution by Mathematica

Time used: 3.739 (sec). Leaf size: 32

DSolve[{3*(2*x-y[x]+2)+(2*x-y[x]+5)*D[y[x],x]==0,{y[-1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {9}{5} W\left (\frac {1}{9} e^{\frac {25 x}{9}+\frac {26}{9}}\right )+2 x+\frac {16}{5} \]