76.12.8 problem 8

Internal problem ID [17493]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 8
Date solved : Monday, March 31, 2025 at 04:15:45 PM
CAS classification : [NONE]

\begin{align*} y^{\prime \prime }-\frac {t}{y}&=\frac {1}{\pi } \end{align*}

With initial conditions

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

✗ Maple

ode:=diff(diff(y(t),t),t)-t/y(t) = 1/Pi; 
ic:=y(0) = y__0, D(y)(0) = y__1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 9

ode=D[y[t],{t,2}]-t/y[t]==1/Pi; 
ic={y[0]==y0,Derivative[1][y][0]==y1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\pi t \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t/y(t) + Derivative(y(t), (t, 2)) - 1/pi,0) 
ics = {y(0): y__0, Subs(Derivative(y(t), t), t, 0): y__1} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : solve: Cannot solve -t/y(t) + Derivative(y(t), (t, 2)) - 1/pi