75.12.14 problem 288

Internal problem ID [16880]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 288
Date solved : Tuesday, January 28, 2025 at 09:39:17 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 1.265 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.096 (sec). Leaf size: 65

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

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