89.23.29 problem 33

Internal problem ID [24833]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Miscellaneous Exercises at page 162
Problem number : 33
Date solved : Thursday, October 02, 2025 at 10:48:26 PM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x) = 2*x; 
ic:=[y(0) = 0, y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {1}{2} x^{2}-\frac {1}{2} x \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to \frac {1}{2} (x-1) x \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{2}}{2} - \frac {x}{2} \]