83.4.18 problem 18

Internal problem ID [19090]
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. Exercise II (C) at page 12
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 12:54:25 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.304 (sec). Leaf size: 13

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

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