29.4.3 problem 90

Internal problem ID [4694]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 90
Date solved : Monday, January 27, 2025 at 09:31:57 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 3.810 (sec). Leaf size: 48

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

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