60.2.151 problem 727

Internal problem ID [10738]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 727
Date solved : Tuesday, January 28, 2025 at 05:10:10 PM
CAS classification : [`x=_G(y,y')`]

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

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 37

dsolve(diff(y(x),x) = (2*x+2+y(x))/(ln(y(x))+2*x-1)*y(x)/(x+1),y(x), singsol=all)
 

\begin{align*} y &= -2 x -2 \\ y &= \frac {\operatorname {LambertW}\left (\left (\ln \left (x +1\right )-c_{1} \right ) {\mathrm e}^{-2 x}\right )}{\ln \left (x +1\right )-c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.408 (sec). Leaf size: 66

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

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