7.4.28 problem 28

Internal problem ID [100]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 28
Date solved : Friday, February 07, 2025 at 07:49:25 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

\[ x = \frac {\arctan \left (y \right ) y^{2}}{2}+y^{2} c_1 +\frac {\arctan \left (y \right )}{2}+c_1 +\frac {y}{2} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 30

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

\[ x(y)\to \frac {1}{2} \left (\left (y^2+1\right ) \arctan (y)+2 c_1 y^2+y+2 c_1\right ) \]