60.2.188 problem 764

Internal problem ID [10775]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 764
Date solved : Tuesday, January 28, 2025 at 05:13:30 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 40

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

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

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 70

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

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