78.24.2 problem 3 (b)

Internal problem ID [18459]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 9. Laplace transforms. Section 51. Derivatives and Integrals of Laplace Transforms. Problems at page 467
Problem number : 3 (b)
Date solved : Tuesday, January 28, 2025 at 08:28:38 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y&=3 \,{\mathrm e}^{-x} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.242 (sec). Leaf size: 37

dsolve([x*diff(y(x),x$2)+(2*x+3)*diff(y(x),x)+(x+3)*y(x)=3*exp(-x),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {x \left (\delta \left (2, 0\right )+\delta \left (1, 0\right )\right ) {\mathrm e}^{-x}-\delta \left (x \right )-\delta \left (1, x\right )}{\delta \left (2, 0\right )+\delta \left (1, 0\right )} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

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