83.8.6 problem 6

Internal problem ID [19132]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 08:30:12 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: 0.512 (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: 0.236 (sec). Leaf size: 12

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

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