60.2.303 problem 880

Internal problem ID [10890]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 880
Date solved : Monday, January 27, 2025 at 10:21:28 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{\prime }&=-\frac {2 a}{-y-2 a -2 a y^{4}+16 a^{2} x y^{2}-32 a^{3} x^{2}-2 a y^{6}+24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 41

dsolve(diff(y(x),x) = -2*a/(-y(x)-2*a-2*a*y(x)^4+16*a^2*x*y(x)^2-32*a^3*x^2-2*a*y(x)^6+24*y(x)^4*a^2*x-96*y(x)^2*a^3*x^2+128*a^4*x^3),y(x), singsol=all)
 

\[ \frac {y}{2 a}+\frac {\int _{}^{-4 a x +y^{2}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a}}{8 a^{2}}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.451 (sec). Leaf size: 291

DSolve[D[y[x],x] == (-2*a)/(-2*a - 32*a^3*x^2 + 128*a^4*x^3 - y[x] + 16*a^2*x*y[x]^2 - 96*a^3*x^2*y[x]^2 - 2*a*y[x]^4 + 24*a^2*x*y[x]^4 - 2*a*y[x]^6),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{4 a^2 \left (K[2]^6-12 a x K[2]^4+K[2]^4+48 a^2 x^2 K[2]^2-8 a x K[2]^2-64 a^3 x^3+16 a^2 x^2+1\right )}-\frac {2 a \int _1^x-\frac {-6 K[2]^5+48 a K[1] K[2]^3-4 K[2]^3-96 a^2 K[1]^2 K[2]+16 a K[1] K[2]}{2 a \left (-K[2]^6+12 a K[1] K[2]^4-K[2]^4-48 a^2 K[1]^2 K[2]^2+8 a K[1] K[2]^2+64 a^3 K[1]^3-16 a^2 K[1]^2-1\right )^2}dK[1]-1}{2 a}\right )dK[2]+\int _1^x\frac {1}{2 a \left (-y(x)^6+12 a K[1] y(x)^4-y(x)^4-48 a^2 K[1]^2 y(x)^2+8 a K[1] y(x)^2+64 a^3 K[1]^3-16 a^2 K[1]^2-1\right )}dK[1]=c_1,y(x)\right ] \]