Internal problem ID [5404]
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: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=x \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-y(x)=x*exp(3*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+\frac {\left (4 x -3\right ) {\mathrm e}^{3 x}}{32} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[y''[x]-y[x]==x*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{32} e^{3 x} (4 x-3)+c_1 e^x+c_2 e^{-x} \]