20.4.6 problem Problem 14

Internal problem ID [3641]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 14
Date solved : Monday, January 27, 2025 at 07:49:23 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

dsolve(x*diff(y(x),x)-y(x)=sqrt(9*x^2+y(x)^2),y(x), singsol=all)
 

\[ \frac {-c_{1} x^{2}+y \left (x \right )+\sqrt {9 x^{2}+y \left (x \right )^{2}}}{x^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.335 (sec). Leaf size: 27

DSolve[x*D[y[x],x]-y[x]==Sqrt[9*x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-c_1} \left (-9+e^{2 c_1} x^2\right ) \]