26.1.3 problem 1.c

Internal problem ID [4243]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 7, page 37
Problem number : 1.c
Date solved : Monday, January 27, 2025 at 08:43:54 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x^{2} y^{\prime }&=3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x \end{align*}

✓ Solution by Maple

Time used: 0.023 (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)
 

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

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 37

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

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