Internal problem ID [13224]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.2 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \sin \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)+y(x)=0,sin(x)],y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (x \right )+c_{2} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 16
DSolve[y''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos (x)+c_2 \sin (x) \]