60.2.258 problem 834

Internal problem ID [10845]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 834
Date solved : Tuesday, January 28, 2025 at 05:24:21 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {\left (x^{4}+3 x y^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x \left (1+x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 68

dsolve(diff(y(x),x) = (x^4+3*x*y(x)^2+3*y(x)^2)/(6*y(x)^2+x)*y(x)/x/(x+1),y(x), singsol=all)
 

\[ \frac {y^{2} x}{6 y^{2}+x} = \frac {\left ({\mathrm e}^{\operatorname {RootOf}\left (x^{2} {\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {x \left ({\mathrm e}^{\textit {\_Z}}+9\right )}{\left (x +1\right )^{2}}\right )+3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-2 x \,{\mathrm e}^{\textit {\_Z}}+9\right )}+9\right ) x}{54} \]

✓ Solution by Mathematica

Time used: 0.481 (sec). Leaf size: 86

DSolve[D[y[x],x] == (y[x]*(x^4 + 3*y[x]^2 + 3*x*y[x]^2))/(x*(1 + x)*(x + 6*y[x]^2)),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {\int _1^x-\frac {6 y(x)}{K[1]^2}dK[1]{}^2}{2 \int _1^x-\frac {6}{K[1]^2}dK[1]}+\int _1^x\left (-\frac {3 y(x)^2}{K[1]^2}-K[1]-\frac {1}{K[1]+1}+1\right )dK[1]+\frac {3 y(x)^2}{x}+\log (y(x))=c_1,y(x)\right ] \]