1.20 problem 5(a)

Internal problem ID [2539]

Book: Elementary Differential equations, Chaundy, 1969
Section: Exercises 3, page 60
Problem number: 5(a).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\sqrt {x^{2}+1}\, y^{\prime }+y-2 x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 34

dsolve(sqrt(1+x^2)*diff(y(x),x)+y(x)=2*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: 0.136 (sec). Leaf size: 39

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

\begin{align*} y(x)\to \left (\sqrt {x^2+1}-x\right ) \left (x \left (\sqrt {x^2+1}+x\right )-\sinh ^{-1}(x)+c_1\right ) \\ \end{align*}