78.9.1 problem 1 (a and b)

Internal problem ID [18249]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 14. Introduction. Problems at page 112
Problem number : 1 (a and b)
Date solved : Tuesday, January 28, 2025 at 11:44:15 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(x*diff(y(x),x$2)- diff(y(x),x)=3*x^2,y(x), singsol=all)
 

\[ y = x^{3}+\frac {1}{2} c_{1} x^{2}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 20

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

\[ y(x)\to x^3+\frac {c_1 x^2}{2}+c_2 \]