32.2.11 problem Differential equations with Linear Coefficients. Exercise 8.11, page 69

Internal problem ID [5795]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number : Differential equations with Linear Coefficients. Exercise 8.11, page 69
Date solved : Monday, January 27, 2025 at 01:19:06 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+\left (3 x +3 y-4\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.241 (sec). Leaf size: 19

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

\[ y \left (x \right ) = \frac {2 \operatorname {LambertW}\left (-1, -\frac {3 \,{\mathrm e}^{x -\frac {5}{2}}}{2}\right )}{3}-x +2 \]

✗ Solution by Mathematica

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

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

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