20.3.7 problem Problem 7

Internal problem ID [3616]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 7
Date solved : Monday, January 27, 2025 at 07:47:39 AM
CAS classification : [_linear]

\begin{align*} 2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve(2*(cos(x)^2)*diff(y(x),x)+y(x)*sin(2*x)=4*cos(x)^4,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 15

DSolve[2*(Cos[x]^2)*D[y[x],x]+y[x]*Sin[2*x]==4*Cos[x]^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x) (2 \sin (x)+c_1) \]