Internal problem ID [11278]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 52.
Summary. Page 117
Problem number: Ex 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=2 x^{3}-x \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=2*x^3-x*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = -48+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{-x}+\frac {\left (1-2 x \right ) {\mathrm e}^{3 x}}{32}+2 x^{3}-12 x^{2}+36 x \]
✓ Solution by Mathematica
Time used: 0.335 (sec). Leaf size: 48
DSolve[y''[x]+2*y'[x]+y[x]==2*x^3-x*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 \left (x^3-6 x^2+18 x-24\right )+\frac {1}{32} e^{3 x} (1-2 x)+e^{-x} (c_2 x+c_1) \]