Internal problem ID [4329]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page
422
Problem number: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y-4 \,{\mathrm e}^{x}-\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=4*exp(x)+(1-x)*(exp(2*x)-1),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} c_{1}+\frac {\left (-3 x +5\right ) {\mathrm e}^{2 x}}{27}+x +{\mathrm e}^{x}-3 \]
✓ Solution by Mathematica
Time used: 0.221 (sec). Leaf size: 38
DSolve[y''[x]+2*y'[x]+y[x]==4*Exp[x]+(1-x)*(Exp[2*x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{27} e^{2 x} (5-3 x)+e^x+x+e^{-x} (c_2 x+c_1)-3 \\ \end{align*}