83.5.14 problem 14

Internal problem ID [19109]
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 (D) at page 16
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 12:57:12 PM
CAS classification : [_linear]

\begin{align*} 1+y+x^{2} y+\left (x^{3}+x \right ) y^{\prime }&=0 \end{align*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve((1+y(x)+x^2*y(x))+(x+x^3)*diff(y(x),x)=0,y(x), singsol=all)
 
\[ y \left (x \right ) = \frac {-\arctan \left (x \right )+c_{1}}{x} \]

Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 16

DSolve[(1+y[x]+x^2*y[x])+(x+x^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \frac {-\arctan (x)+c_1}{x} \]