60.2.177 problem 753

Internal problem ID [10764]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 753
Date solved : Tuesday, January 28, 2025 at 05:13:10 PM
CAS classification : [`x=_G(y,y')`]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 38

dsolve(diff(y(x),x) = (x+1+x^4*ln(y(x)))*y(x)*ln(y(x))/x/(x+1),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {12 x}{3 x^{4}-4 x^{3}+6 x^{2}+12 \ln \left (x +1\right )-12 c_{1} -12 x}} \]

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 102

DSolve[D[y[x],x] == (Log[y[x]]*(1 + x + x^4*Log[y[x]])*y[x])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
 

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