60.2.398 problem 975

Internal problem ID [10985]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 975
Date solved : Monday, January 27, 2025 at 10:38:38 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

\begin{align*} y^{\prime }&=y^{3}+x^{2} y^{2}+\frac {y x^{4}}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 59

dsolve(diff(y(x),x) = y(x)^3+x^2*y(x)^2+1/3*y(x)*x^4+1/27*x^6-2/3*x,y(x), singsol=all)
 

\begin{align*} y &= -\frac {x^{2} \sqrt {-54 c_{1} -2 x}-3}{3 \sqrt {-54 c_{1} -2 x}} \\ y &= -\frac {x^{2} \sqrt {-54 c_{1} -2 x}+3}{3 \sqrt {-54 c_{1} -2 x}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.191 (sec). Leaf size: 58

DSolve[D[y[x],x] == (-2*x)/3 + x^6/27 + (x^4*y[x])/3 + x^2*y[x]^2 + y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^2}{3}-\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to -\frac {x^2}{3}+\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to -\frac {x^2}{3} \\ \end{align*}