29.12.10 problem 329

Internal problem ID [4929]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 329
Date solved : Monday, January 27, 2025 at 09:51:38 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} 2 x^{2} y^{\prime }+1+2 y x -x^{2} y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

dsolve(2*x^2*diff(y(x),x)+1+2*x*y(x)-x^2*y(x)^2 = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.886 (sec). Leaf size: 61

DSolve[2 x^2 D[y[x],x]+1+2 x y[x]- x^2 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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