Internal problem ID [14885]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 64.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }-3 y=x \,{\mathrm e}^{x}} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 56
Order:=6; dsolve(diff(y(x),x$2)+2*diff(y(x),x)-3*y(x)=x*exp(x),y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {3}{2} x^{2}-x^{3}+\frac {7}{8} x^{4}-\frac {1}{2} x^{5}\right ) y \left (0\right )+\left (x -x^{2}+\frac {7}{6} x^{3}-\frac {5}{6} x^{4}+\frac {61}{120} x^{5}\right ) D\left (y \right )\left (0\right )+\frac {x^{3}}{6}+\frac {x^{5}}{20}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 66
AsymptoticDSolveValue[y''[x]+2*y'[x]-3*y[x]==x*Exp[x],y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{2}+\frac {7 x^4}{8}-x^3+\frac {3 x^2}{2}+1\right )+c_2 \left (\frac {61 x^5}{120}-\frac {5 x^4}{6}+\frac {7 x^3}{6}-x^2+x\right ) \]