29.3.17 problem 71

Internal problem ID [4679]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 71
Date solved : Monday, January 27, 2025 at 09:31:16 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(x),x) = sin(x)*(2*sec(x)^2-y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = -2 \,\operatorname {Ei}_{1}\left (\cos \left (x \right )\right ) {\mathrm e}^{\cos \left (x \right )}+{\mathrm e}^{\cos \left (x \right )} c_{1} +2 \sec \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.115 (sec). Leaf size: 28

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

\[ y(x)\to 2 e^{\cos (x)} \operatorname {ExpIntegralEi}(-\cos (x))+2 \sec (x)+c_1 e^{\cos (x)} \]