Internal problem ID [3593]
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]
\[ \boxed {4 \left (x^{2}+1\right ) y^{\prime }-4 y x=x^{2}} \]
✓ 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: 0.098 (sec). Leaf size: 50
DSolve[4(1+x^2)y'[x]-4 x y[x]-x^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{4} \sqrt {x^2+1} \log \left (\sqrt {x^2+1}-x\right )+c_1 \sqrt {x^2+1}-\frac {x}{4} \]