Internal problem ID [11811]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=3 x^{2}-4 \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve([diff(y(x),x$2)+y(x)=3*x^2-4*sin(x),y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \left (2 x +6\right ) \cos \left (x \right )+3 x^{2}-\sin \left (x \right )-6 \]
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 23
DSolve[{y''[x]+y[x]==3*x^2-4*Sin[x],{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x^2-\sin (x)+2 (x+3) \cos (x)-6 \]