67.2.31 problem Problem 5(e)

Internal problem ID [13917]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 5(e)
Date solved : Monday, March 31, 2025 at 08:18:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y&=1 \end{align*}

With initial conditions

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

✗ Maple

ode:=sin(x)*diff(diff(y(x),x),x)+x*diff(y(x),x)+7*y(x) = 1; 
ic:=y(1) = 1, D(y)(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=Sin[x]*D[y[x],{x,2}]+x*D[y[x],x]+7*y[x]==1; 
ic={y[1]==1,Derivative[1][y][1]==0}; 
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) + 7*y(x) + sin(x)*Derivative(y(x), (x, 2)) - 1,0) 
ics = {y(1): 1, Subs(Derivative(y(x), x), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-7*y(x) - sin(x)*Derivative(y(x), (x, 2)) + 1)/x cannot be solved by the factorable group method