15.8.32 problem 33

Internal problem ID [3035]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 33
Date solved : Monday, January 27, 2025 at 07:10:01 AM
CAS classification : [_exact]

\begin{align*} 2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 y x -y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.084 (sec). Leaf size: 30

dsolve((2*x*tan(y(x))+3*y(x)^2+x^2)+(x^2*sec(y(x))^2+6*x*y(x)-y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \tan \left (y\right ) x^{2}+\frac {x^{3}}{3}+3 y^{2} x -\frac {y^{3}}{3}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.494 (sec). Leaf size: 87

DSolve[(2*x*Tan[y[x]]+3*y[x]^2+x^2)+(x^2*Sec[y[x]]^2+6*x*y[x]-y[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{3} x^3 \sec ^2(y(x))+\frac {1}{3} x^3 \cos (2 y(x)) \sec ^2(y(x))+x^2 \sin (2 y(x)) \sec ^2(y(x))-\frac {2 y(x)^3}{3}+3 x y(x)^2 \sec ^2(y(x))+3 x y(x)^2 \cos (2 y(x)) \sec ^2(y(x))=c_1,y(x)\right ] \]