60.2.394 problem 971

Internal problem ID [10981]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 971
Date solved : Monday, January 27, 2025 at 10:38:28 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {\left (y x +1\right )^{3}}{x^{5}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 70

dsolve(diff(y(x),x) = (x*y(x)+1)^3/x^5,y(x), singsol=all)
 

\[ y = \frac {-2+x^{3} \left (\tan \left (\operatorname {RootOf}\left (18 x^{3} \left (-\frac {1}{x^{6}}\right )^{{2}/{3}}+6 \sqrt {3}\, \textit {\_Z} -3 \ln \left (3\right )+\ln \left (\left (\sqrt {3}\, \sin \left (\textit {\_Z} \right )+3 \cos \left (\textit {\_Z} \right )\right )^{6}\right )-18 c_{1} \right )\right ) \sqrt {3}+1\right ) \left (-\frac {1}{x^{6}}\right )^{{1}/{3}}}{2 x} \]

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 61

DSolve[D[y[x],x] == (1 + x*y[x])^3/x^5,y[x],x,IncludeSingularSolutions -> True]
 

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