Internal problem ID [3135]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 389.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } \sqrt {x^{2}+1}-2 x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 34
dsolve(diff(y(x),x)*sqrt(x^2+1) = 2*x-y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}+x \sqrt {x^{2}+1}-\arcsinh \relax (x )+c_{1}}{x +\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 84
DSolve[y'[x] Sqrt[1+x^2]==2 x -y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\tanh ^{-1}\left (\frac {x}{\sqrt {x^2+1}}\right )} \left (x \sqrt {\frac {1}{x^2+1}} \left (x \left (\sqrt {x^2+1}+x\right )+1\right )-\log \left (\sqrt {\frac {1}{x^2+1}} x^2+\sqrt {\frac {1}{x^2+1}}+x\right )+c_1\right ) \\ \end{align*}