77.1.17 problem 32 (page 40)

Internal problem ID [17907]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 32 (page 40)
Date solved : Tuesday, January 28, 2025 at 11:12:05 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{2} (\sin (x)+(x+2 c_1) \sec (x)) \]