87.10.4 problem 4

Internal problem ID [23405]
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 2. Linear differential equations. Exercise at page 79
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:41:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1-x \right ) y^{\prime \prime }-x y^{\prime }+y \,{\mathrm e}^{x}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=4 \\ \end{align*}

✗ Maple

ode:=(1-x)*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x)*exp(x) = 0; 
ic:=[y(0) = 0, D(y)(0) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(1-x)*D[y[x],{x,2}]-x*D[y[x],x]+Exp[x]*y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] ==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

False