Internal problem ID [3084]
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]
\[ \boxed {4 \left (x^{2}+1\right ) y^{\prime }-4 y x -x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(4*(x^2+1)*diff(y(x),x)-4*x*y(x)-x^2 = 0,y(x), singsol=all)
\[ y \left (x \right ) = \left (-\frac {x}{4 \sqrt {x^{2}+1}}+\frac {\operatorname {arcsinh}\left (x \right )}{4}+c_{1} \right ) \sqrt {x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 30
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} (\text {arcsinh}(x)+4 c_1)\right ) \\ \end{align*}