65.5.1 problem 10.1 (i)

Internal problem ID [13740]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number : 10.1 (i)
Date solved : Tuesday, January 28, 2025 at 06:00:24 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 49

dsolve((2*x*y(x)- sec(x)^2)+(x^2+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {x^{2}}{2}-\frac {\sqrt {x^{4}+4 \tan \left (x \right )-4 c_{1}}}{2} \\ y &= -\frac {x^{2}}{2}+\frac {\sqrt {x^{4}+4 \tan \left (x \right )-4 c_{1}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 22.561 (sec). Leaf size: 90

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

\begin{align*} y(x)\to \frac {1}{2} \left (-x^2-\sqrt {\sec ^2(x)} \sqrt {\cos ^2(x) \left (x^4+4 \tan (x)+4 c_1\right )}\right ) \\ y(x)\to \frac {1}{2} \left (-x^2+\sqrt {\sec ^2(x)} \sqrt {\cos ^2(x) \left (x^4+4 \tan (x)+4 c_1\right )}\right ) \\ \end{align*}