60.1.534 problem 537

Internal problem ID [10548]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 537
Date solved : Monday, January 27, 2025 at 08:53:38 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 x^{5} y&=0 \end{align*}

✗ Solution by Maple

dsolve(x^3*diff(y(x),x)^3-3*x^2*y(x)*diff(y(x),x)^2+(3*x*y(x)^2+x^6)*diff(y(x),x)-y(x)^3-2*x^5*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 15

DSolve[-2*x^5*y[x] - y[x]^3 + (x^6 + 3*x*y[x]^2)*D[y[x],x] - 3*x^2*y[x]*D[y[x],x]^2 + x^3*D[y[x],x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x \left (x+c_1{}^2\right ) \]