87.10.9 problem 10

Internal problem ID [23410]
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 : 10
Date solved : Thursday, October 02, 2025 at 09:41:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \cos \left (x \right ) y^{\prime \prime }+3 y&=1 \end{align*}

With initial conditions

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

✗ Maple

ode:=cos(x)*diff(diff(y(x),x),x)+3*y(x) = 1; 
ic:=[y(1) = 0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 2.629 (sec). Leaf size: 6

ode=Cos[x]*D[y[x],{x,2}]+3*y[x]==1; 
ic={y[1]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) + cos(x)*Derivative(y(x), (x, 2)) - 1,0) 
ics = {y(1): 0, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve 3*y(x) + cos(x)*Derivative(y(x), (x, 2)) - 1