86.3.4 problem 4

Internal problem ID [23095]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 4. Linear equations of the first order. Exercise 4a at page 56
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:20:06 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+7 y&={\mathrm e}^{5 x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 17

ode:=diff(y(x),x)+7*y(x) = exp(5*x); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{5 x}}{12}-\frac {{\mathrm e}^{-7 x}}{12} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 21

ode=D[y[x],x]+7*y[x]==Exp[5*x]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{12} e^{-7 x} \left (e^{12 x}-1\right ) \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(7*y(x) - exp(5*x) + Derivative(y(x), x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{5 x}}{12} - \frac {e^{- 7 x}}{12} \]