29.7.23 problem 198

Internal problem ID [4798]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 198
Date solved : Monday, January 27, 2025 at 09:39:35 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 0.301 (sec). Leaf size: 39

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

\[ y(x)\to \frac {1}{2} e^{c_1} x^{a+1}-\frac {1}{2} b^2 e^{-c_1} x^{1-a} \]