78.23.4 problem 3 (d)

Internal problem ID [18455]
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 50. Applications to differential equations. Problems at page 462
Problem number : 3 (d)
Date solved : Tuesday, January 28, 2025 at 11:50:20 AM
CAS classification : [[_2nd_order, _missing_y]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.184 (sec). Leaf size: 23

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

\[ y = 5 \,{\mathrm e}^{-x}-5-3 x^{2}+x^{3}+6 x \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 25

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

\[ y(x)\to x^3-3 x^2+6 x+5 e^{-x}-5 \]