Internal problem ID [6236]
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`]]
\[ \boxed {y^{\prime }-\frac {2 y}{x}-\frac {x^{3}}{y}-x \tan \left (\frac {y}{x^{2}}\right )=0} \]
✓ Solution by Maple
Time used: 1.157 (sec). Leaf size: 176
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 \left (x \right ) &= \frac {x^{2} \left (\csc \left (\operatorname {RootOf}\left (2 c_{1}^{2} \sin \left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 c_{1}^{2} \cos \left (\textit {\_Z} \right )^{2}-4 c_{1} \sin \left (\textit {\_Z} \right ) x \textit {\_Z} +2 x^{2}\right )\right ) x -\cot \left (\operatorname {RootOf}\left (2 c_{1}^{2} \sin \left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 c_{1}^{2} \cos \left (\textit {\_Z} \right )^{2}-4 c_{1} \sin \left (\textit {\_Z} \right ) x \textit {\_Z} +2 x^{2}\right )\right ) c_{1} \right )}{c_{1}} \\ y \left (x \right ) &= \frac {\left (\cot \left (\operatorname {RootOf}\left (2 c_{1}^{2} \sin \left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 c_{1}^{2} \cos \left (\textit {\_Z} \right )^{2}-4 c_{1} \sin \left (\textit {\_Z} \right ) x \textit {\_Z} +2 x^{2}\right )\right ) c_{1} +\csc \left (\operatorname {RootOf}\left (2 c_{1}^{2} \sin \left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 c_{1}^{2} \cos \left (\textit {\_Z} \right )^{2}-4 c_{1} \sin \left (\textit {\_Z} \right ) x \textit {\_Z} +2 x^{2}\right )\right ) x \right ) x^{2}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.103 (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]
\[ \text {Solve}\left [3 \log (x)-\log \left (y(x) \sin \left (\frac {y(x)}{x^2}\right )+x^2 \cos \left (\frac {y(x)}{x^2}\right )\right )=c_1,y(x)\right ] \]