Internal problem ID [5483]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.8. Integrating Factors. Page
32
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 y}{x}-\frac {x^{3}}{y}-x \tan \left (\frac {y}{x^{2}}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 1.239 (sec). Leaf size: 216
dsolve(diff(y(x),x)=2*y(x)/x+x^3/y(x)+x*tan(y(x)/x^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{2} \left (c_{1} \cos \left (\RootOf \left (\textit {\_Z}^{2} c_{1}^{2} \cos \left (2 \textit {\_Z} \right )+4 \textit {\_Z} x c_{1} \sin \left (\textit {\_Z} \right )-\textit {\_Z}^{2} c_{1}^{2}+c_{1}^{2} \cos \left (2 \textit {\_Z} \right )+c_{1}^{2}-2 x^{2}\right )\right )-x \right )}{c_{1} \sin \left (\RootOf \left (\textit {\_Z}^{2} c_{1}^{2} \cos \left (2 \textit {\_Z} \right )+4 \textit {\_Z} x c_{1} \sin \left (\textit {\_Z} \right )-\textit {\_Z}^{2} c_{1}^{2}+c_{1}^{2} \cos \left (2 \textit {\_Z} \right )+c_{1}^{2}-2 x^{2}\right )\right )} \\ y \relax (x ) = \frac {x^{2} \left (c_{1} \cos \left (\RootOf \left (\textit {\_Z}^{2} c_{1}^{2} \cos \left (2 \textit {\_Z} \right )+4 \textit {\_Z} x c_{1} \sin \left (\textit {\_Z} \right )-\textit {\_Z}^{2} c_{1}^{2}+c_{1}^{2} \cos \left (2 \textit {\_Z} \right )+c_{1}^{2}-2 x^{2}\right )\right )+x \right )}{c_{1} \sin \left (\RootOf \left (\textit {\_Z}^{2} c_{1}^{2} \cos \left (2 \textit {\_Z} \right )+4 \textit {\_Z} x c_{1} \sin \left (\textit {\_Z} \right )-\textit {\_Z}^{2} c_{1}^{2}+c_{1}^{2} \cos \left (2 \textit {\_Z} \right )+c_{1}^{2}-2 x^{2}\right )\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.69 (sec). Leaf size: 36
DSolve[y'[x]==2*y[x]/x+x^3/y[x]+x*Tan[y[x]/x^2],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [3 \log (x)-\log \left (y(x) \sin \left (\frac {y(x)}{x^2}\right )+x^2 \cos \left (\frac {y(x)}{x^2}\right )\right )=c_1,y(x)\right ] \]