Internal problem ID [14794]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+y x=\cos \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (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);
\[ y \left (x \right ) = x -\frac {1}{8} x^{4}+\frac {1}{40} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 19
AsymptoticDSolveValue[{y''[x]+y'[x]+x*y[x]==Cos[x],{y[0]==0,y'[0]==1}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{40}-\frac {x^4}{8}+x \]