62.5.1 problem Ex 1

Internal problem ID [12816]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 12. Page 18
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:24:32 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

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

\begin{align*} y &= 0 \\ y &= \frac {\tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right )}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.931 (sec). Leaf size: 71

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

\begin{align*} y(x)\to 0 \\ y(x)\to \frac {i \tan \left (\frac {1}{2} i \log (x)+c_1\right )}{x} \\ y(x)\to 0 \\ y(x)\to \frac {-x+e^{2 i \text {Interval}[\{0,\pi \}]}}{x^2+x e^{2 i \text {Interval}[\{0,\pi \}]}} \\ \end{align*}