86.3.10 problem 8

Internal problem ID [23101]
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 : 8
Date solved : Thursday, October 02, 2025 at 09:21:51 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {6 y}{x}&=7 x \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 15

ode:=diff(y(x),x)-6*y(x)/x = 7*x; 
ic:=[y(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {7}{4} x^{6}-\frac {7}{4} x^{2} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 17

ode=D[y[x],x]-6*y[x]/x==7*x; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {7}{4} x^2 \left (x^4-1\right ) \end{align*}

✓ Sympy. Time used: 0.166 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-7*x + Derivative(y(x), x) - 6*y(x)/x,0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (\frac {7 x^{4}}{4} - \frac {7}{4}\right ) \]