24.1.20 problem 5(a)

Internal problem ID [4209]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 5(a)
Date solved : Monday, January 27, 2025 at 08:42:20 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 34

dsolve(sqrt(1+x^2)*diff(y(x),x)+y(x)=2*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: 0.084 (sec). Leaf size: 33

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

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