29.2.7 problem 32

Internal problem ID [4640]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 2
Problem number : 32
Date solved : Monday, January 27, 2025 at 09:29:04 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 19

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

\[ y(x)\to -\frac {\cos (x)}{3}+c_1 \sec ^2(x) \]