60.2.335 problem 912

Internal problem ID [10922]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 912
Date solved : Monday, January 27, 2025 at 10:24:44 PM
CAS classification : [_rational]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.724 (sec). Leaf size: 305

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

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