15.8.50 problem 53

Internal problem ID [3053]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 53
Date solved : Monday, January 27, 2025 at 07:12:44 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 2.070 (sec). Leaf size: 20

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

\[ y = \frac {5}{2}+\frac {x}{2}+2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-\frac {1}{4}+\frac {x}{4}}}{4}\right ) \]

✓ Solution by Mathematica

Time used: 4.110 (sec). Leaf size: 28

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

\[ y(x)\to \frac {1}{2} \left (4 W\left (-\frac {1}{4} e^{\frac {x-1}{4}}\right )+x+5\right ) \]