15.7.16 problem 16

Internal problem ID [2997]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 16
Date solved : Monday, January 27, 2025 at 07:06:57 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 1.766 (sec). Leaf size: 53

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

\begin{align*} y(x)\to \arctan (2 x (x+2 c_1)) \\ y(x)\to -\frac {\pi \sqrt {x^2}}{2 x} \\ y(x)\to \frac {\pi \sqrt {x^2}}{2 x} \\ \end{align*}