Internal problem ID [3085]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 337.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {4 \left (x^{2}+1\right ) y^{\prime }-4 y x -x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 28
dsolve(4*(x^2+1)*diff(y(x),x)-4*x*y(x)-x^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = \left (-\frac {x}{4 \sqrt {x^{2}+1}}+\frac {\arcsinh \relax (x )}{4}+c_{1}\right ) \sqrt {x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 40
DSolve[4(1+x^2)y'[x]-4 x y[x]-x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-x+\sqrt {x^2+1} \left (\tanh ^{-1}\left (\frac {x}{\sqrt {x^2+1}}\right )+4 c_1\right )\right ) \\ \end{align*}