7.11.2 problem 2

Internal problem ID [323]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 2
Date solved : Wednesday, February 05, 2025 at 03:18:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }+2 y&=3 x +4 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)-diff(y(x),x)+2*y(x)=3*x+4,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {7}\, x}{2}\right ) c_2 +{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {7}\, x}{2}\right ) c_1 +\frac {3 x}{2}+\frac {11}{4} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 56

DSolve[D[y[x],{x,2}]-D[y[x],x]+2*y[x]==3*x+4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 x}{2}+c_2 e^{x/2} \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 e^{x/2} \sin \left (\frac {\sqrt {7} x}{2}\right )+\frac {11}{4} \]