85.9.10 problem 1 (j)

Internal problem ID [22484]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 37
Problem number : 1 (j)
Date solved : Thursday, October 02, 2025 at 08:40:56 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=8 y x +3 y \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 16

ode:=diff(y(x),x) = 8*x*y(x)+3*y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 22

ode=D[y[x],{x,1}]==8*x*y[x]+3*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{x (4 x+3)}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.161 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x*y(x) - 3*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x \left (4 x + 3\right )} \]