38.2.13 problem 13

Internal problem ID [6442]
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
Date solved : Monday, January 27, 2025 at 02:04:15 PM
CAS classification : [_linear]

\begin{align*} -y+x y^{\prime }&=x^{3} \cos \left (x \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 15

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

\[ y(x)\to x (x \sin (x)+\cos (x)+1) \]