36.2.21 problem 21

Internal problem ID [6314]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 21
Date solved : Monday, January 27, 2025 at 01:55:55 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=-\frac {15 \sqrt {2}\, \pi ^{2}}{32} \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 16

dsolve([cos(x)*diff(y(x),x)+y(x)*sin(x)=2*x*cos(x)^2,y(1/4*Pi) = -15/32*2^(1/2)*Pi^2],y(x), singsol=all)
 

\[ y \left (x \right ) = \left (-\pi ^{2}+x^{2}\right ) \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 17

DSolve[{Cos[x]*D[y[x],x]+y[x]*Sin[x]==2*x*Cos[x]^2,{y[Pi/4]==-15*Sqrt[2]*Pi^2/32}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^2-\pi ^2\right ) \cos (x) \]