85.33.51 problem 51

Internal problem ID [22674]
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 65
Problem number : 51
Date solved : Thursday, October 02, 2025 at 09:05:26 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x) = 2*y(x)+3*x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.070 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} e^{2 x} - \frac {3 x}{2} - \frac {3}{4} \]