85.7.1 problem 1 (a)

Internal problem ID [22455]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 32
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 08:39:46 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 17

ode:=diff(y(x),x) = 2*y(x)+3*x; 
ic:=[y(1) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {3 x}{2}-\frac {3}{4}+\frac {25 \,{\mathrm e}^{-2+2 x}}{4} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 23

ode=D[y[x],{x,1}]==3*x+2*y[x]; 
ic={y[1]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} \left (-6 x+25 e^{2 x-2}-3\right ) \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x - 2*y(x) + Derivative(y(x), x),0) 
ics = {y(1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {3 x}{2} + \frac {25 e^{2 x}}{4 e^{2}} - \frac {3}{4} \]