Internal problem ID [5627]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }+4 y-x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2, y^{\prime }\relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.119 (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)
\[ y \relax (x ) = \frac {\left (\left (\sin \left (\frac {\sqrt {15}}{2}\right ) \sqrt {15}+135 \cos \left (\frac {\sqrt {15}}{2}\right )\right ) \cos \left (\frac {\sqrt {15}\, x}{2}\right )-\sin \left (\frac {\sqrt {15}\, x}{2}\right ) \left (\cos \left (\frac {\sqrt {15}}{2}\right ) \sqrt {15}-135 \sin \left (\frac {\sqrt {15}}{2}\right )\right )\right ) {\mathrm e}^{\frac {x}{2}-\frac {1}{2}}}{80}+\frac {x}{4}+\frac {1}{16} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 60
DSolve[{y''[x]-y'[x]+4*y[x]==x,{y[1]==2,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{80} \left (20 x+e^{\frac {x-1}{2}} \left (135 \cos \left (\frac {1}{2} \sqrt {15} (x-1)\right )-\sqrt {15} \sin \left (\frac {1}{2} \sqrt {15} (x-1)\right )\right )+5\right ) \\ \end{align*}