40.2.13 problem 38

Internal problem ID [6591]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 38
Date solved : Monday, January 27, 2025 at 02:14:38 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} 2 x y^{\prime }-2 y&=\sqrt {x^{2}+4 y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 30

dsolve(2*x*diff(y(x),x)-2*y(x)= sqrt(x^2+4*y(x)^2),y(x), singsol=all)
 

\[ \frac {-c_1 \,x^{2}+\sqrt {x^{2}+4 y^{2}}+2 y}{x^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.341 (sec). Leaf size: 18

DSolve[2*x*D[y[x],x]-2*y[x]== Sqrt[x^2+4*y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x \sinh (\log (x)+2 c_1) \]