62.4.1 problem Ex 1

Internal problem ID [12813]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 11. Equations in which M and N are linear but not homogeneous. Page 16
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:24:24 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 4 x +3 y+1+\left (x +y+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 1.085 (sec). Leaf size: 29

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

\[ y = -3-\frac {\left (x -2\right ) \left (2 \operatorname {LambertW}\left (c_{1} \left (x -2\right )\right )+1\right )}{\operatorname {LambertW}\left (c_{1} \left (x -2\right )\right )} \]

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 73

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

\[ \text {Solve}\left [\int _1^{-\frac {(-1)^{2/3} \left (\frac {3 (x-2)}{x+y(x)+1}+2\right )}{\sqrt [3]{2}}}\frac {2}{2 K[1]^3+3 \sqrt [3]{-2} K[1]+2}dK[1]=\frac {1}{9} (-2)^{2/3} \log (x-2)+c_1,y(x)\right ] \]