74.16.18 problem 20

Internal problem ID [16524]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 09:10:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

Using series method with expansion around

\begin{align*} 0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

Order:=6; 
dsolve([diff(y(x),x$2)+diff(y(x),x)+x*y(x)=cos(x),y(0) = 0, D(y)(0) = 1],y(x),type='series',x=0);
 

\[ y = x -\frac {1}{8} x^{4}+\frac {1}{40} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 19

AsymptoticDSolveValue[{D[y[x],{x,2}]+D[y[x],x]+x*y[x]==Cos[x],{y[0]==0,Derivative[1][y][0] ==1}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {x^5}{40}-\frac {x^4}{8}+x \]