13.13 problem 13

Internal problem ID [12797]

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: 13.
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y=-x^{2}+1} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}

✓ Solution by Maple

Time used: 5.0 (sec). Leaf size: 18

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

\[ y \left (x \right ) = -x -\frac {x^{2}}{2}+\cos \left (x \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 20

DSolve[{y''[x]-2*y'[x]+2*y[x]==1-x^2,{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to e^x \cos (x)-\frac {1}{2} x (x+2) \]