10.6.25 problem 25

Internal problem ID [1242]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 25
Date solved : Monday, January 27, 2025 at 04:47:18 AM
CAS classification : [_exact, _rational]

\begin{align*} \frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

dsolve(2*x/y(x)-y(x)/(x^2+y(x)^2)+(-x^2/y(x)^2+x/(x^2+y(x)^2))*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ y = \cot \left (\operatorname {RootOf}\left (-\textit {\_Z} +x \tan \left (\textit {\_Z} \right )+c_1 \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.292 (sec). Leaf size: 23

DSolve[2*x/y[x]-y[x]/(x^2+y[x]^2)+(-x^2/y[x]^2+x/(x^2+y[x]^2))*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\arctan \left (\frac {x}{y(x)}\right )-\frac {x^2}{y(x)}=c_1,y(x)\right ] \]