14.3 problem 9

Internal problem ID [12801]

Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number: 9.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

\[ \boxed {y^{\prime \prime }+9 y=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}

✓ Solution by Maple

Time used: 4.921 (sec). Leaf size: 12

dsolve([diff(y(x),x$2)+9*y(x)=1,y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\cos \left (3 x \right )}{9}+\frac {1}{9} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 17

DSolve[{y''[x]+9*y[x]==1,{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to \frac {2}{9} \sin ^2\left (\frac {3 x}{2}\right ) \]