2.13 problem 13

Internal problem ID [4591]

Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 13.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {x y^{\prime }-y-x^{3} \cos \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \left (\pi \right ) = 0] \end {align*}

Solution by Maple

Time used: 0.008 (sec). Leaf size: 14

dsolve([x*diff(y(x),x)-y(x)=x^3*cos(x),y(Pi) = 0],y(x), singsol=all)
 

\[ y \relax (x ) = \left (\cos \relax (x )+\sin \relax (x ) x +1\right ) x \]

Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 15

DSolve[{x*y'[x]-y[x]==x^3*Cos[x],{y[Pi]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x (x \sin (x)+\cos (x)+1) \\ \end{align*}