Internal problem ID [4705]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page
248
Problem number: Problem 24.37.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y-{\mathrm e}^{x} x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 2, y^{\prime \prime }\relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 16
dsolve([diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=x^2*exp(x),y(0) = 1, D(y)(0) = 2, (D@@2)(y)(0) = 3],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{x} \left (x^{5}+60 x +60\right )}{60} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 20
DSolve[{y'''[x]-3*y''[x]+3*y'[x]-y[x]==x^2*Exp[x],{y[0]==1,y'[0]==2,y''[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{60} e^x \left (x^5+60 x+60\right ) \\ \end{align*}