60.1.295 problem 296

Internal problem ID [10309]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 296
Date solved : Monday, January 27, 2025 at 07:07:32 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 x^{2} y^{2}+x^{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 61

dsolve(x*(y(x)^2+x^2*y(x)+x^2)*diff(y(x),x)-2*y(x)^3-2*x^2*y(x)^2+x^4=0,y(x), singsol=all)
 

\begin{align*} y &= -c_{1} x^{2}-\sqrt {x^{2} \left (1+\left (c_{1}^{2}-c_{1} \right ) x^{2}\right )} \\ y &= -c_{1} x^{2}+\sqrt {x^{2} \left (1+\left (c_{1}^{2}-c_{1} \right ) x^{2}\right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.793 (sec). Leaf size: 88

DSolve[x*(y[x]^2+x^2*y[x]+x^2)*D[y[x],x]-2*y[x]^3-2*x^2*y[x]^2+x^4==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -e^{-c_1} \left (x^2+\sqrt {x^2 \left (x^2-e^{c_1} x^2+e^{2 c_1}\right )}\right ) \\ y(x)\to e^{-c_1} \left (-x^2+\sqrt {x^2 \left (x^2-e^{c_1} x^2+e^{2 c_1}\right )}\right ) \\ \end{align*}