73.4.25 problem 5.3 (e)

Internal problem ID [15107]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.3 (e)
Date solved : Tuesday, January 28, 2025 at 07:30:59 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 10

dsolve([x*diff(y(x),x)=y(x)+x^2*cos(x),y(1/2*Pi) = 0],y(x), singsol=all)
 

\[ y = \left (\sin \left (x \right )-1\right ) x \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 21

DSolve[{x*D[y[x],x]==y[x]+x^2*Cos[x],{y[Pi/2]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \int _{\frac {\pi }{2}}^x\cos (K[1])dK[1] \]