60.1.301 problem 302

Internal problem ID [10315]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 302
Date solved : Monday, January 27, 2025 at 07:08:08 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.216 (sec). Leaf size: 137

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

\begin{align*} y &= -\frac {\sqrt {2}\, \sqrt {x c_{1} \left (2 c_{1} +x -\sqrt {x \left (4 c_{1} +x \right )}\right )}}{2 c_{1} x} \\ y &= \frac {\sqrt {2}\, \sqrt {x c_{1} \left (2 c_{1} +x -\sqrt {x \left (4 c_{1} +x \right )}\right )}}{2 c_{1} x} \\ y &= -\frac {\sqrt {2}\, \sqrt {x c_{1} \left (2 c_{1} +x +\sqrt {x \left (4 c_{1} +x \right )}\right )}}{2 c_{1} x} \\ y &= \frac {\sqrt {2}\, \sqrt {x c_{1} \left (2 c_{1} +x +\sqrt {x \left (4 c_{1} +x \right )}\right )}}{2 c_{1} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.297 (sec). Leaf size: 65

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

\begin{align*} y(x)\to \frac {1}{2} \left (c_1-\frac {\sqrt {4+c_1{}^2 x}}{\sqrt {x}}\right ) \\ y(x)\to \frac {1}{2} \left (\frac {\sqrt {4+c_1{}^2 x}}{\sqrt {x}}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}