83.5.2 problem 2

Internal problem ID [19097]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 12:55:56 PM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

\[ y \left (x \right ) = \tan \left (x \right )-1+{\mathrm e}^{-\tan \left (x \right )} c_{1} \]

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 18

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

\[ y(x)\to \tan (x)+c_1 e^{-\tan (x)}-1 \]