67.2.30 problem Problem 5(d)

Internal problem ID [13908]
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(d)
Date solved : Wednesday, March 05, 2025 at 10:21:57 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

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

✗ Maple

ode:=x*diff(diff(y(x),x),x)+2*x^2*diff(y(x),x)+y(x)*sin(x) = sinh(x); 
ic:=y(0) = 1, D(y)(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^2*D[y[x],{x,2}]+2*x^2*D[y[x],x]+y[x]*Sin[x]==Sinh[x]; 
ic={y[0]==1,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

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