78.24.1 problem 3 (a)

Internal problem ID [18458]
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 (a)
Date solved : Tuesday, January 28, 2025 at 11:50:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y&=0 \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: 0.194 (sec). Leaf size: 12

dsolve([x*diff(y(x),x$2)+(3*x-1)*diff(y(x),x)-(4*x+9)*y(x)=0,y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \frac {c_{1} {\mathrm e}^{x} x^{2}}{2} \]

✓ Solution by Mathematica

Time used: 0.287 (sec). Leaf size: 14

DSolve[{x*D[y[x],{x,2}]+(3*x-1)*D[y[x],x]-(4*x+9)*y[x]==0,{y[0]==0,Derivative[1][y][0] == 0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^x x^2 \]