1.3 problem 1.c

Internal problem ID [2573]

Book: Differential equations with applications and historial notes, George F. Simmons, 1971
Section: Chapter 2, section 7, page 37
Problem number: 1.c.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]

Solve \begin {gather*} \boxed {y^{\prime } x^{2}-3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )-y x=0} \end {gather*}

Solution by Maple

Time used: 0.022 (sec). Leaf size: 12

dsolve(x^2*diff(y(x),x)=3*(x^2+y(x)^2)*arctan(y(x)/x)+x*y(x),y(x), singsol=all)
 

\[ y \relax (x ) = \tan \left (c_{1} x^{3}\right ) x \]

Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 37

DSolve[x^2*y'[x]==3*(x^2+y[x]^2)*Arctan[y[x]/x]+x*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{\text {Arctan}(K[1]) \left (K[1]^2+1\right )}dK[1]=3 \log (x)+c_1,y(x)\right ] \]