Internal problem ID [4320]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page
422
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+y^{\prime }-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(2*diff(y(x),x$2)+diff(y(x),x)=2*x,y(x), singsol=all)
\[ y \relax (x ) = -2 \,{\mathrm e}^{-\frac {x}{2}} c_{1}+x^{2}-4 x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 22
DSolve[y''[x]+y'[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x-2) x-c_1 e^{-x}+c_2 \\ \end{align*}