60.2.399 problem 976

Internal problem ID [10986]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 976
Date solved : Tuesday, January 28, 2025 at 05:40:20 PM
CAS classification : [_rational, _Abel]

\begin{align*} y^{\prime }&=\frac {y \left (y^{2} x^{7}+y x^{4}+x -3\right )}{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 70

dsolve(diff(y(x),x) = y(x)/x*(y(x)^2*x^7+y(x)*x^4+x-3),y(x), singsol=all)
 

\[ y = \frac {\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (3\right )+\sqrt {3}\, \ln \left (7\right )-\sqrt {3}\, \ln \left (-\frac {1}{-2+\sqrt {3}\, \sin \left (2 \textit {\_Z} \right )+\cos \left (2 \textit {\_Z} \right )}\right )+3 \sqrt {3}\, c_{1} -2 \sqrt {3}\, x -2 \textit {\_Z} \right )\right )-1}{2 x^{3}} \]

✓ Solution by Mathematica

Time used: 1.160 (sec). Leaf size: 82

DSolve[D[y[x],x] == (y[x]*(-3 + x + x^4*y[x] + x^7*y[x]^2))/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {3 y(x) x^6+x^3}{\sqrt [3]{7} \sqrt [3]{-x^9}}}\frac {1}{K[1]^3-\frac {6 \sqrt [3]{-1} K[1]}{7^{2/3}}+1}dK[1]=\frac {7^{2/3} \left (-x^9\right )^{2/3}}{9 x^5}+c_1,y(x)\right ] \]