60.1.259 problem 260

Internal problem ID [10273]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 260
Date solved : Monday, January 27, 2025 at 06:42:53 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 59

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

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

✓ Solution by Mathematica

Time used: 0.726 (sec). Leaf size: 79

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

\begin{align*} y(x)\to \frac {x}{-2 x^2+\frac {\sqrt {x (-2 \log (x)+4+c_1)}}{\sqrt {\frac {1}{x^3}}}} \\ y(x)\to -\frac {x}{2 x^2+\frac {\sqrt {x (-2 \log (x)+4+c_1)}}{\sqrt {\frac {1}{x^3}}}} \\ y(x)\to 0 \\ \end{align*}