Internal problem ID [2169]
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: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sin \left (x \right ) {\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)+y(x)=exp(x)*sin(x),y(0) = 3, D(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-2 \,{\mathrm e}^{x}+17\right ) \cos \left (x \right )}{5}+\frac {\sin \left (x \right ) \left ({\mathrm e}^{x}+11\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 28
DSolve[{y''[x]+y[x]==Exp[x]*Sin[x],{y[0]==3,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} \left (\left (e^x+11\right ) \sin (x)+\left (17-2 e^x\right ) \cos (x)\right ) \]