60.2.397 problem 974

Internal problem ID [10984]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 974
Date solved : Monday, January 27, 2025 at 10:38:36 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Abel]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 57

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

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

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 46

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

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