Internal problem ID [6380]
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]]
\[ \boxed {y^{\prime \prime }-y^{\prime }+4 y=x} \] With initial conditions \begin {align*} [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.344 (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)
\[ y \left (x \right ) = \frac {\left (\left (\sqrt {15}\, \sin \left (\frac {\sqrt {15}}{2}\right )+135 \cos \left (\frac {\sqrt {15}}{2}\right )\right ) \cos \left (\frac {\sqrt {15}\, x}{2}\right )-\sin \left (\frac {\sqrt {15}\, x}{2}\right ) \left (\sqrt {15}\, \cos \left (\frac {\sqrt {15}}{2}\right )-135 \sin \left (\frac {\sqrt {15}}{2}\right )\right )\right ) {\mathrm e}^{\frac {x}{2}-\frac {1}{2}}}{80}+\frac {x}{4}+\frac {1}{16} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 67
DSolve[{y''[x]-y'[x]+4*y[x]==x,{y[1]==2,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{80} \left (20 x-\sqrt {15} e^{\frac {x-1}{2}} \sin \left (\frac {1}{2} \sqrt {15} (x-1)\right )+135 e^{\frac {x-1}{2}} \cos \left (\frac {1}{2} \sqrt {15} (x-1)\right )+5\right ) \]