39.1.8 problem Problem 11.8

Internal problem ID [6513]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.8
Date solved : Monday, January 27, 2025 at 02:11:07 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=9 x^{2}+2 x -1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)=9*x^2+2*x-1,y(x), singsol=all)
 

\[ y = \frac {3}{4} x^{4}+\frac {1}{3} x^{3}-\frac {1}{2} x^{2}+c_1 x +c_2 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]==9*x^2+2*x-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 x^4}{4}+\frac {x^3}{3}-\frac {x^2}{2}+c_2 x+c_1 \]