Internal problem ID [2798]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of
Parameters Method. page 556
Problem number: Problem 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=F \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=F(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (\int {\mathrm e}^{-x} F \left (x \right )d x \right ) {\mathrm e}^{3 x}+3 c_{1} {\mathrm e}^{3 x}-\left (\int F \left (x \right ) {\mathrm e}^{2 x}d x \right )+3 c_{2} \right ) {\mathrm e}^{-2 x}}{3} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 68
DSolve[y''[x]+y'[x]-2*y[x]==F[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (\int _1^x-\frac {1}{3} e^{2 K[1]} F(K[1])dK[1]+e^{3 x} \int _1^x\frac {1}{3} e^{-K[2]} F(K[2])dK[2]+c_2 e^{3 x}+c_1\right ) \]