82.12.3 problem Ex. 3

Internal problem ID [18768]
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. 3
Date solved : Tuesday, January 28, 2025 at 08:29:17 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 1.426 (sec). Leaf size: 28

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

\[ \ln \left (y \left (x \right )+\sqrt {x^{2}+y \left (x \right )^{2}}\right )-\ln \left (x \right )-x -c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.249 (sec). Leaf size: 12

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

\[ y(x)\to x \sinh (x+c_1) \]