Internal problem ID [5375]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page
92
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=4 x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-y(x)=4*x*exp(x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+\left (x -1\right ) x \,{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 30
DSolve[y''[x]-y[x]==4*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (x^2-x+\frac {1}{2}+c_1\right )+c_2 e^{-x} \]