29.4.4 problem 91

Internal problem ID [4695]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 91
Date solved : Monday, January 27, 2025 at 09:32:00 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 48

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

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

✓ Solution by Mathematica

Time used: 0.365 (sec). Leaf size: 49

DSolve[D[y[x],x]+y[x]^3 Sec[x] Tan[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {2} \sqrt {\sec (x)-c_1}} \\ y(x)\to \frac {1}{\sqrt {2} \sqrt {\sec (x)-c_1}} \\ y(x)\to 0 \\ \end{align*}