Internal problem ID [4652]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Further problems 25. page 1094
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 \sin \relax (x )+4 y=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = 0, y^{\prime }\left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)=3*sin(x)-4*y(x),y(0) = 0, D(y)(1/2*Pi) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\sin \left (2 x \right )}{2}+\sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 13
DSolve[{y''[x]==3*Sin[x]-4*y[x],{y[0]==0,y'[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -(\sin (x) (\cos (x)-1)) \\ \end{align*}