39.5.14 problem Problem 24.37

Internal problem ID [6556]
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
Date solved : Monday, January 27, 2025 at 02:12:13 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=x^{2} {\mathrm e}^{x} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ y^{\prime \prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.167 (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)
 

\[ y = \frac {{\mathrm e}^{x} \left (x^{5}+60 x +60\right )}{60} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 20

DSolve[{D[y[x],{x,3}]-3*D[y[x],{x,2}]+3*D[y[x],x]-y[x]==x^2*Exp[x],{y[0]==1,Derivative[1][y][0] ==2,Derivative[2][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{60} e^x \left (x^5+60 x+60\right ) \]