60.2.202 problem 778

Internal problem ID [10789]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 778
Date solved : Tuesday, January 28, 2025 at 05:13:39 PM
CAS classification : [_rational, _Abel]

\begin{align*} y^{\prime }&=\frac {-3 x^{2} y+1+y^{2} x^{6}+y^{3} x^{9}}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

dsolve(diff(y(x),x) = (-3*x^2*y(x)+1+y(x)^2*x^6+y(x)^3*x^9)/x^3,y(x), singsol=all)
 

\[ y = \frac {-3+29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1} \right )}{9 x^{3}} \]

✓ Solution by Mathematica

Time used: 1.147 (sec). Leaf size: 73

DSolve[D[y[x],x] == (1 - 3*x^2*y[x] + x^6*y[x]^2 + x^9*y[x]^3)/x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {3 y(x) x^6+x^3}{\sqrt [3]{29} \sqrt [3]{x^9}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {29^{2/3} \left (x^9\right )^{2/3}}{9 x^5}+c_1,y(x)\right ] \]