8.11.6 problem 6

Internal problem ID [874]
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
Date solved : Wednesday, February 05, 2025 at 04:36:10 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }+4 y^{\prime }+7 y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (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)
 

\[ y = {\mathrm e}^{-x} \sin \left (\frac {\sqrt {10}\, x}{2}\right ) c_2 +{\mathrm e}^{-x} \cos \left (\frac {\sqrt {10}\, x}{2}\right ) c_1 +\frac {x^{2}}{7}-\frac {8 x}{49}+\frac {4}{343} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 56

DSolve[2*D[y[x],{x,2}]+4*D[y[x],x]+7*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{343} \left (49 x^2-56 x+4\right )+c_2 e^{-x} \cos \left (\sqrt {\frac {5}{2}} x\right )+c_1 e^{-x} \sin \left (\sqrt {\frac {5}{2}} x\right ) \]