88.22.11 problem 15

Internal problem ID [24171]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 160 (Laplace transform)
Problem number : 15
Date solved : Thursday, October 02, 2025 at 10:00:25 PM
CAS classification : [[_2nd_order, _missing_y]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=-{\frac {1}{2}} \\ \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 10

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x) = 2*x; 
ic:=[y(0) = 0, D(y)(0) = -1/2]; 
dsolve([ode,op(ic)],y(x),method='laplace');
 

\[ y = \frac {x \left (x -1\right )}{2} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 13

ode=D[y[x],{x,2}]+2*D[y[x],x]==2*x; 
ic={y[0]==0,Derivative[1][y][0] ==-1/2}; 
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, Subs(Derivative(y(x), x), x, 0): -1/2} 
dsolve(ode,func=y(x),ics=ics)
 

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