60.2.182 problem 758

Internal problem ID [10769]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 758
Date solved : Tuesday, January 28, 2025 at 05:13:16 PM
CAS classification : [`x=_G(y,y')`]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 61

dsolve(diff(y(x),x) = (2*x+2+x^3*y(x))/(ln(y(x))+2*x-1)*y(x)/(x+1),y(x), singsol=all)
 

\[ y = -\frac {6 \operatorname {LambertW}\left (-\frac {\left (-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )+6 c_{1} -6 x \right ) {\mathrm e}^{-2 x}}{6}\right )}{-2 x^{3}+3 x^{2}+6 \ln \left (x +1\right )+6 c_{1} -6 x} \]

✓ Solution by Mathematica

Time used: 0.397 (sec). Leaf size: 86

DSolve[D[y[x],x] == (y[x]*(2 + 2*x + x^3*y[x]))/((1 + x)*(-1 + 2*x + Log[y[x]])),y[x],x,IncludeSingularSolutions -> True]
 

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