58.9.7 problem 8

Internal problem ID [14686]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 124
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:50:12 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=4 x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 4*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} c_1 +{\mathrm e}^{x} c_2 +2 x^{2}+6 x +7 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 29

ode=D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==4*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x^2+6 x+c_1 e^x+c_2 e^{2 x}+7 \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**2 + 2*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{2 x} + 2 x^{2} + 6 x + 7 \]