64.5.14 problem 14

Internal problem ID [13327]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 05:22:21 AM
CAS classification : [_linear]

\begin{align*} y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve((y(x)*sin(2*x)-cos(x))+(1+sin(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 29

DSolve[(y[x]*Sin[2*x]-Cos[x])+(1+Sin[x]^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\int _1^x-2 \cos (K[1])dK[1]+c_1}{\cos (2 x)-3} \]