60.1.309 problem 310

Internal problem ID [10323]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 310
Date solved : Monday, January 27, 2025 at 07:08:41 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.110 (sec). Leaf size: 125

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

\begin{align*} y &= -\frac {\sqrt {-10 c_{1} x^{2}-2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ y &= \frac {\sqrt {-10 c_{1} x^{2}-2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ y &= -\frac {\sqrt {-10 c_{1} x^{2}+2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ y &= \frac {\sqrt {-10 c_{1} x^{2}+2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 23.966 (sec). Leaf size: 295

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

\begin{align*} y(x)\to -\frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ \end{align*}