15.2.21 problem 21

Internal problem ID [2891]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 21
Date solved : Monday, January 27, 2025 at 06:26:00 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.048 (sec). Leaf size: 32

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

\[ -c_1 +y^{k -1} \sqrt {x^{2}+y^{2}}+y^{k -1} x = 0 \]

✓ Solution by Mathematica

Time used: 0.248 (sec). Leaf size: 59

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

\[ \text {Solve}\left [\frac {1}{2} \left ((k-1) \log \left (\sqrt {\frac {y(x)^2}{x^2}+1}-1\right )+(k+1) \log \left (\sqrt {\frac {y(x)^2}{x^2}+1}+1\right )\right )=-k \log (x)+c_1,y(x)\right ] \]