Internal problem ID [5385]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 15. Linear equations with constant coefficients (Variation of parameters).
Supplemetary problems. Page 98
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y=2+{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+2*y(x)=2+exp(x),y(x), singsol=all)
\[ y = c_{1} \cos \left (\sqrt {2}\, x \right )+c_{2} \sin \left (\sqrt {2}\, x \right )+1+\frac {{\mathrm e}^{x}}{3} \]
✓ Solution by Mathematica
Time used: 0.216 (sec). Leaf size: 36
DSolve[y''[x]+2*y[x]==2+Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{3}+c_1 \cos \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {2} x\right )+1 \]