75.12.35 problem 309

Internal problem ID [16901]
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 : 309
Date solved : Tuesday, January 28, 2025 at 09:40:20 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+1+\left (2 x +2 y-1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.381 (sec). Leaf size: 20

dsolve([(x+y(x)+1)+(2*x+2*y(x)-1)*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.633 (sec). Leaf size: 28

DSolve[{(x+y[x]+1)+(2*x+2*y[x]-1)*D[y[x],x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3}{2} W\left (\frac {2}{3} e^{\frac {x+1}{3}}\right )-x+2 \]