87.10.5 problem 5

Internal problem ID [23406]
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 : 5
Date solved : Thursday, October 02, 2025 at 09:41:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+y&=2 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {3 \pi }{4}\right )&=1 \\ y^{\prime }\left (\frac {3 \pi }{4}\right )&=1 \\ \end{align*}

✗ Maple

ode:=sin(x)*diff(diff(y(x),x),x)+x*diff(y(x),x)+y(x) = 2; 
ic:=[y(3/4*Pi) = 1, D(y)(3/4*Pi) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=Sin[x]*D[y[x],{x,2}]+x*D[y[x],x]+y[x]==2; 
ic={y[3*Pi/4]==1,Derivative[1][y][3*Pi/4] ==1}; 
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) + y(x) + sin(x)*Derivative(y(x), (x, 2)) - 2,0) 
ics = {y(3*pi/4): 1, Subs(Derivative(y(x), x), x, 3*pi/4): 1} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-y(x) - sin(x)*Derivative(y(x), (x, 2)) +