85.36.9 problem 4 (a)

Internal problem ID [22737]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 171
Problem number : 4 (a)
Date solved : Thursday, October 02, 2025 at 09:14:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = x^2; 
ic:=[y(0) = 0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {7}{4}+\frac {3 x}{2}+\frac {x^{2}}{2}+\frac {{\mathrm e}^{2 x}}{4}-2 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to \frac {1}{4} \left (2 x^2+6 x-8 e^x+e^{2 x}+7\right ) \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \frac {x^{2}}{2} + \frac {3 x}{2} + \frac {e^{2 x}}{4} - 2 e^{x} + \frac {7}{4} \]