7.7.35 problem 35

Internal problem ID [213]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 35
Date solved : Monday, January 27, 2025 at 02:42:07 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 y x +2 x}{x^{2}+1} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

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

\[ y = c_1 \,x^{2}+c_1 -1 \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 20

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

\begin{align*} y(x)\to -1+c_1 \left (x^2+1\right ) \\ y(x)\to -1 \\ \end{align*}