6.27 problem 33

Internal problem ID [4325]

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: 33.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+y-x^{3}+1-2 \cos \relax (x )-\left (2-4 x \right ) {\mathrm e}^{x}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 33

dsolve(diff(y(x),x$2)+y(x)=x^3-1+2*cos(x)+(2-4*x)*exp(x),y(x), singsol=all)
 

\[ y \relax (x ) = c_{2} \sin \relax (x )+c_{1} \cos \relax (x )+x^{3}+\left (-2 \,{\mathrm e}^{x}+\sin \relax (x )-6\right ) x +\cos \relax (x )+3 \,{\mathrm e}^{x}-1 \]

Solution by Mathematica

Time used: 0.286 (sec). Leaf size: 38

DSolve[y''[x]+y[x]==x^3-1+2*Cos[x]+(2-4*x)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^3-6 x+e^x (3-2 x)+\left (\frac {1}{2}+c_1\right ) \cos (x)+(x+c_2) \sin (x)-1 \\ \end{align*}