60.2.322 problem 899

Internal problem ID [10909]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 899
Date solved : Monday, January 27, 2025 at 10:23:24 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=\frac {32 x^{5}+64 x^{6}+64 y^{2} x^{6}+32 y x^{4}+4 x^{2}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{64 x^{8}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 47

dsolve(diff(y(x),x) = 1/64*(32*x^5+64*x^6+64*y(x)^2*x^6+32*y(x)*x^4+4*x^2+64*x^6*y(x)^3+48*x^4*y(x)^2+12*x^2*y(x)+1)/x^8,y(x), singsol=all)
 

\[ y = \frac {116 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right ) x +3 c_{1} x -1\right ) x^{2}-12 x^{2}-9}{36 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.191 (sec). Leaf size: 84

DSolve[D[y[x],x] == (1/64 + x^2/16 + x^5/2 + x^6 + (3*x^2*y[x])/16 + (x^4*y[x])/2 + (3*x^4*y[x]^2)/4 + x^6*y[x]^2 + x^6*y[x]^3)/x^8,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {\frac {4 x^2+3}{4 x^4}+\frac {3 y(x)}{x^2}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^6}}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=-\frac {1}{9} 29^{2/3} \left (\frac {1}{x^6}\right )^{2/3} x^3+c_1,y(x)\right ] \]