Internal problem ID [12798]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number: 14.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }=x +\cos \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1, y^{\prime \prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 5.36 (sec). Leaf size: 34
dsolve([diff(y(x),x$3)+3*diff(y(x),x$2)+2*diff(y(x),x)=x+cos(x),y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {3 \cos \left (x \right )}{10}+\frac {\sin \left (x \right )}{10}-\frac {{\mathrm e}^{-x}}{2}-\frac {3 x}{4}+\frac {x^{2}}{4}+\frac {17 \,{\mathrm e}^{-2 x}}{40}+\frac {11}{8} \]
✓ Solution by Mathematica
Time used: 0.565 (sec). Leaf size: 41
DSolve[{y'''[x]+3*y''[x]+2*y'[x]==x+Cos[x],{y[0]==1,y'[0]==-1,y''[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{40} \left (10 x^2-30 x+17 e^{-2 x}-20 e^{-x}+4 \sin (x)-12 \cos (x)+55\right ) \]