24.1.21 problem 5(b)

Internal problem ID [4210]
Book : Elementary Differential equations, Chaundy, 1969
Section : Exercises 3, page 60
Problem number : 5(b)
Date solved : Monday, January 27, 2025 at 08:42:22 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 32

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

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

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 31

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

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