83.3.4 problem 4

Internal problem ID [19060]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (B) at page 9
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 12:49:45 PM
CAS classification : [_separable]

\begin{align*} 2 y+\left (x^{2}+1\right ) \arctan \left (x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 10

dsolve(y(x)+(1+x^2)*arctan(x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1}}{\arctan \left (x \right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.135 (sec). Leaf size: 17

DSolve[y[x]+(1+x^2)*ArcTan[x]*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{\arctan (x)^2} \\ y(x)\to 0 \\ \end{align*}