Internal problem ID [5160]
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]]
\[ \boxed {y^{\prime \prime }+4 y=3 \sin \left (x \right )} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 0, y^{\prime }\left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = -\frac {\sin \left (2 x \right )}{2}+\sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.021 (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]
\[ y(x)\to -(\sin (x) (\cos (x)-1)) \]