64.11.1 problem 1

Internal problem ID [13451]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 05:42:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+8 y&=4 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 40

dsolve(diff(y(x),x$2)-3*diff(y(x),x)+8*y(x)=4*x^2,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {23}\, x}{2}\right ) c_{2} +{\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {23}\, x}{2}\right ) c_{1} +\frac {x^{2}}{2}+\frac {3 x}{8}+\frac {1}{64} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 63

DSolve[D[y[x],{x,2}]-3*D[y[x],x]+8*y[x]==4*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2}{2}+\frac {3 x}{8}+c_2 e^{3 x/2} \cos \left (\frac {\sqrt {23} x}{2}\right )+c_1 e^{3 x/2} \sin \left (\frac {\sqrt {23} x}{2}\right )+\frac {1}{64} \]