29.12.18 problem 337

Internal problem ID [4937]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 337
Date solved : Monday, January 27, 2025 at 09:52:47 AM
CAS classification : [_linear]

\begin{align*} 4 \left (x^{2}+1\right ) y^{\prime }-4 y x -x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(4*(x^2+1)*diff(y(x),x)-4*x*y(x)-x^2 = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (4 c_{1} +\operatorname {arcsinh}\left (x \right )\right ) \sqrt {x^{2}+1}}{4}-\frac {x}{4} \]

✓ Solution by Mathematica

Time used: 0.120 (sec). Leaf size: 38

DSolve[4(1+x^2)D[y[x],x]-4 x y[x]-x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (\sqrt {x^2+1} \text {arcsinh}(x)+4 c_1 \sqrt {x^2+1}-x\right ) \]