50.14.10 problem 2(b)

Internal problem ID [8048]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 2(b)
Date solved : Monday, January 27, 2025 at 03:38:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.194 (sec). Leaf size: 73

dsolve([diff(y(x),x$2)-diff(y(x),x)+4*y(x)=x,y(1) = 2, D(y)(1) = 1],y(x), singsol=all)
 

\[ y = \frac {\left (\left (\sin \left (\frac {\sqrt {15}}{2}\right ) \sqrt {15}+135 \cos \left (\frac {\sqrt {15}}{2}\right )\right ) \cos \left (\frac {\sqrt {15}\, x}{2}\right )-\sin \left (\frac {\sqrt {15}\, x}{2}\right ) \left (\sqrt {15}\, \cos \left (\frac {\sqrt {15}}{2}\right )-135 \sin \left (\frac {\sqrt {15}}{2}\right )\right )\right ) {\mathrm e}^{-\frac {1}{2}+\frac {x}{2}}}{80}+\frac {x}{4}+\frac {1}{16} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 67

DSolve[{D[y[x],{x,2}]-D[y[x],x]+4*y[x]==x,{y[1]==2,Derivative[1][y][1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{80} \left (20 x-\sqrt {15} e^{\frac {x-1}{2}} \sin \left (\frac {1}{2} \sqrt {15} (x-1)\right )+135 e^{\frac {x-1}{2}} \cos \left (\frac {1}{2} \sqrt {15} (x-1)\right )+5\right ) \]