82.12.25 problem Ex. 27

Internal problem ID [18790]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Examples on chapter II at page 29
Problem number : Ex. 27
Date solved : Tuesday, January 28, 2025 at 12:17:30 PM
CAS classification : [_linear]

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

Solution by Maple

Time used: 0.000 (sec). Leaf size: 36

dsolve(sqrt(a^2+x^2)*diff(y(x),x)+y(x)=sqrt(a^2+x^2)-x,y(x), singsol=all)
 
\[ y \left (x \right ) = \frac {a^{2} \ln \left (x +\sqrt {a^{2}+x^{2}}\right )+c_{1}}{x +\sqrt {a^{2}+x^{2}}} \]

Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 42

DSolve[Sqrt[a^2+x^2]*D[y[x],x]+y[x]==Sqrt[a^2+x^2]-x,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \frac {a^2 \log \left (\sqrt {a^2+x^2}+x\right )+c_1}{\sqrt {a^2+x^2}+x} \]