Internal problem ID [224]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 y^{\prime \prime }+4 y^{\prime }+7 y=x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
dsolve(2*diff(y(x),x$2)+4*diff(y(x),x)+7*y(x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \sin \left (\frac {\sqrt {10}\, x}{2}\right ) c_{2} +{\mathrm e}^{-x} \cos \left (\frac {\sqrt {10}\, x}{2}\right ) c_{1} +\frac {x^{2}}{7}-\frac {8 x}{49}+\frac {4}{343} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 56
DSolve[2*y''[x]+4*y'[x]+7*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{343} \left (49 x^2-56 x+4\right )+c_2 e^{-x} \cos \left (\sqrt {\frac {5}{2}} x\right )+c_1 e^{-x} \sin \left (\sqrt {\frac {5}{2}} x\right ) \]