83.4.17 problem 17

Internal problem ID [19089]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 12:54:23 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 20

dsolve((2*x+4*y(x)+3)*diff(y(x),x)=(2*y(x)+x+1),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: 4.092 (sec). Leaf size: 39

DSolve[(2*x+4*y[x]+3)*D[y[x],x]==(2*y[x]+x+1),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*}