Internal problem ID [4811]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y=2 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)+y(x)=2*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right )+\cos \left (x \right ) c_{1} +{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 19
DSolve[y''[x]+y[x]==2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x+c_1 \cos (x)+c_2 \sin (x) \]