28.1.15 problem 15

Internal problem ID [4321]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 15
Date solved : Monday, January 27, 2025 at 09:02:28 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3+2 x +4 y\right ) y^{\prime }&=1+x +2 y \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 20

dsolve((3+2*x+4*y(x))*diff(y(x),x)=1+x+2*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {x}{2}+\frac {\operatorname {LambertW}\left (c_{1} {\mathrm e}^{5+8 x}\right )}{8}-\frac {5}{8} \]

✓ Solution by Mathematica

Time used: 4.001 (sec). Leaf size: 39

DSolve[(3+2*x+4*y[x])*D[y[x],x]==1+x+2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{8} \left (W\left (-e^{8 x-1+c_1}\right )-4 x-5\right ) \\ y(x)\to \frac {1}{8} (-4 x-5) \\ \end{align*}