Internal problem ID [234]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-2 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 18
dsolve([diff(y(x),x$2)+4*y(x)=2*x,y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {3 \sin \left (2 x \right )}{4}+\cos \left (2 x \right )+\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 22
DSolve[{y''[x]+4*y[x]==2*x,{y[0]==1,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (2 x)+\frac {1}{2} (x+3 \sin (x) \cos (x)) \\ \end{align*}