45.1.4 problem 2. direct method

Internal problem ID [9501]
Book : A course in Ordinary Differential Equations. by Stephen A. Wirkus, Randall J. Swift. CRC Press NY. 2015. 2nd Edition
Section : Chapter 8. Series Methods. section 8.2. The Power Series Method. Problems Page 603
Problem number : 2. direct method
Date solved : Tuesday, September 30, 2025 at 06:19:43 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 22

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

\[ y = -\frac {x^{2}}{2}-\frac {x}{2}-\frac {1}{4}+\frac {9 \,{\mathrm e}^{-2+2 x}}{4} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to e^{2 x-2} \left (e^2 \int _1^xe^{-2 K[1]} K[1]^2dK[1]+1\right ) \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = - \frac {x^{2}}{2} - \frac {x}{2} + \frac {9 e^{2 x}}{4 e^{2}} - \frac {1}{4} \]