87.4.24 problem 35

Internal problem ID [23290]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 37
Problem number : 35
Date solved : Thursday, October 02, 2025 at 09:28:47 PM
CAS classification : [_linear]

\begin{align*} \left (x -1\right ) y^{\prime }-3 y&=\left (x -1\right )^{5} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=16 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 19

ode:=(x-1)*diff(y(x),x)-3*y(x) = (x-1)^5; 
ic:=[y(-1) = 16]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (x^{2}-2 x -7\right ) \left (x -1\right )^{3}}{2} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 22

ode=(x-1)*D[y[x],x]-3*y[x]==(x-1)^5; 
ic={y[-1]==16}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} (x-1)^3 \left (x^2-2 x-7\right ) \end{align*}

✓ Sympy. Time used: 0.296 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x - 1)**5 + (x - 1)*Derivative(y(x), x) - 3*y(x),0) 
ics = {y(-1): 16} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{5}}{2} - \frac {5 x^{4}}{2} + x^{3} + 7 x^{2} - \frac {19 x}{2} + \frac {7}{2} \]