29.2.9 problem 34

Internal problem ID [4642]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 34
Date solved : Monday, January 27, 2025 at 09:29:11 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(diff(y(x),x) = csc(x)+3*y(x)*tan(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \sec \left (x \right )^{3} \left (\frac {\cos \left (x \right )^{2}}{2}+\ln \left (\sin \left (x \right )\right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.059 (sec). Leaf size: 24

DSolve[D[y[x],x]==Csc[x]+3 y[x] Tan[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sec ^3(x) \left (-\frac {1}{2} \sin ^2(x)+\log (\sin (x))+c_1\right ) \]