Internal problem ID [2173]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {8 y^{\prime \prime }-y=x \,{\mathrm e}^{-\frac {x}{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 43
dsolve([8*diff(y(x),x$2)-y(x)=x*exp(-x/2),y(0) = 3, D(y)(0) = 5],y(x), singsol=all)
\[ y = \frac {\left (-5-16 \sqrt {2}\right ) {\mathrm e}^{-\frac {\sqrt {2}\, x}{4}}}{2}+\frac {\left (-5+16 \sqrt {2}\right ) {\mathrm e}^{\frac {\sqrt {2}\, x}{4}}}{2}+\left (x +8\right ) {\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 83
DSolve[{8*y''[x]-y[x]==x*Exp[-x/2],{y[0]==3,y'[0]==5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-\frac {1}{4} \left (2+\sqrt {2}\right ) x} \left (2 e^{\frac {x}{2 \sqrt {2}}} (x+8)-\left (5+16 \sqrt {2}\right ) e^{x/2}+\left (16 \sqrt {2}-5\right ) e^{\frac {1}{2} \left (1+\sqrt {2}\right ) x}\right ) \]