29.8.7 problem 212

Internal problem ID [4812]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 212
Date solved : Monday, January 27, 2025 at 09:40:41 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x y^{\prime }&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 10

dsolve(x*diff(y(x),x) = (1+y(x)^2)*(x^2+arctan(y(x))),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.357 (sec). Leaf size: 14

DSolve[x D[y[x],x]==(1+y[x]^2)(x^2+ArcTan[y[x]]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \tan (x (x+2 c_1)) \]