Internal problem ID [2171]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=3 \sin \left (x \right ) x} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve([diff(y(x),x$2)+y(x)=3*x*sin(x),y(0) = 2, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right )+2 \cos \left (x \right )-\frac {3 \cos \left (x \right ) x^{2}}{4}+\frac {3 x \sin \left (x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 28
DSolve[{y''[x]+y[x]==3*x*Sin[x],{y[0]==2,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (2-\frac {3 x^2}{4}\right ) \cos (x)+\left (\frac {3 x}{4}+1\right ) \sin (x) \]