Internal problem ID [4324]
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]]
\[ \boxed {y^{\prime \prime }+y-x^{3}+1-2 \cos \left (x \right )-\left (2-4 x \right ) {\mathrm e}^{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+y(x)=x^3-1+2*cos(x)+(2-4*x)*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right )+c_{1} \cos \left (x \right )+\left (-2 x +3\right ) {\mathrm e}^{x}+x^{3}+x \sin \left (x \right )-6 x +\cos \left (x \right )-1 \]
✓ 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*}