19.3.4 problem 12

Internal problem ID [3547]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:41:28 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x y^{\prime }&=\sqrt {16 x^{2}-y^{2}}+y \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve(x*diff(y(x),x)=sqrt(16*x^2-y(x)^2)+y(x),y(x), singsol=all)
 

\[ -\arctan \left (\frac {y \left (x \right )}{\sqrt {16 x^{2}-y \left (x \right )^{2}}}\right )+\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.405 (sec). Leaf size: 18

DSolve[x*D[y[x],x]==Sqrt[16*x^2-y[x]^2]+y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -4 x \cosh (i \log (x)+c_1) \]