Internal problem ID [5393]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary
problems. Page 107
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)-y(x)=exp(x),y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x}+\frac {x \,{\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 29
DSolve[y''[x]-y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (\frac {x}{2}-\frac {1}{4}+c_1\right )+c_2 e^{-x} \]