6.2.33 problem 33

Internal problem ID [1569]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 33
Date solved : Tuesday, September 30, 2025 at 04:36:42 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 14

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

\[ y = \frac {1}{2}+\frac {5 \,{\mathrm e}^{-x^{2}}}{2} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to \frac {5 e^{-x^2}}{2}+\frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.228 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {1}{2} + \frac {5 e^{- x^{2}}}{2} \]