67.7.48 problem 48

Internal problem ID [16493]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 48
Date solved : Thursday, October 02, 2025 at 01:35:29 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=x \left (6 y+{\mathrm e}^{x^{2}}\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(x),x) = x*(6*y(x)+exp(x^2)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{x^{2}}}{4}+{\mathrm e}^{3 x^{2}} c_1 \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 25

ode=D[y[x],x]==x*(6*y[x]+Exp[x^2]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^{x^2}}{4}+c_1 e^{3 x^2} \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(6*y(x) + exp(x**2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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