84.16.9 problem 8.18

Internal problem ID [22189]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 8. Linear first-order differential equations. Supplementary problems
Problem number : 8.18
Date solved : Thursday, October 02, 2025 at 08:33:49 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 17

ode:=diff(y(x),x)+2*x*y(x) = 2*x^3; 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.156 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**3 + 2*x*y(x) + Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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