Internal problem ID [13371]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x -y=\cos \left (x \right ) x^{2}} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \left (\sin \left (x \right )-1\right ) x \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 11
DSolve[{x*y'[x]==y[x]+x^2*Cos[x],{y[Pi/2]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (\sin (x)-1) \]