87.10.12 problem 13

Internal problem ID [23413]
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 : 13
Date solved : Thursday, October 02, 2025 at 09:41:27 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 x y^{\prime \prime }-7 \cos \left (x \right ) y^{\prime }+y&={\mathrm e}^{-x} \end{align*}

✗ Maple

ode:=2*x*diff(diff(y(x),x),x)-7*cos(x)*diff(y(x),x)+y(x) = exp(-x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=2*x*D[y[x],{x,2}]-7*Cos[x]*D[y[x],x]+y[x]==Exp[-x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), (x, 2)) + y(x) - 7*cos(x)*Derivative(y(x), x) - exp(-x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -((2*x*Derivative(y(x), (x, 2)) + y(x))*exp(x) - 1)*exp(-x)/(7*c