29.14.8 problem 389

Internal problem ID [4987]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 389
Date solved : Monday, January 27, 2025 at 10:01:21 AM
CAS classification : [_linear]

\begin{align*} y^{\prime } \sqrt {x^{2}+1}&=2 x -y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 33

DSolve[D[y[x],x] Sqrt[1+x^2]==2 x -y[x],y[x],x,IncludeSingularSolutions -> True]
 

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