Internal problem ID [11265]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 50. Method
of undetermined coefficients. Page 107
Problem number: Ex 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=2 \,{\mathrm e}^{x}+x^{3}-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+y(x)=2*exp(x)+x^3-x,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )+x^{3}+{\mathrm e}^{x}-7 x \]
✓ Solution by Mathematica
Time used: 0.234 (sec). Leaf size: 25
DSolve[y''[x]+y[x]==2*Exp[x]+x^3-x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3-7 x+e^x+c_1 \cos (x)+c_2 \sin (x) \]