85.84.4 problem 3

Internal problem ID [23015]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 10. Systems of differential equations and their applications. B Exercises at page 445
Problem number : 3
Date solved : Sunday, October 12, 2025 at 05:55:06 AM
CAS classification : system_of_ODEs

\begin{align*} t^{2} \left (\frac {d^{2}}{d t^{2}}y \left (t \right )\right )+t \left (\frac {d}{d t}z \left (t \right )\right )+z \left (t \right )&=t\\ t \left (\frac {d}{d t}y \left (t \right )\right )+z \left (t \right )&=\ln \left (t \right ) \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 31

ode:=[t^2*diff(diff(y(t),t),t)+t*diff(z(t),t)+z(t) = t, t*diff(y(t),t)+z(t) = ln(t)]; 
dsolve(ode);
 

\begin{align*} y \left (t \right ) &= \frac {\ln \left (t \right )^{2}}{4}-\frac {t}{2}+\frac {\ln \left (t \right )}{2}+c_1 \\ z \left (t \right ) &= \frac {\ln \left (t \right )}{2}+\frac {t}{2}-\frac {1}{2} \\ \end{align*}

✗ Mathematica

ode={t^2*D[y[t],{t,2}]+t*D[z[t],t]+z[t]==t,t*D[y[t],{t,1}]+z[t]==Log[t]}; 
ic={}; 
DSolve[{ode,ic},{y[t],z[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
z = Function("z") 
ode=[Eq(t**2*Derivative(y(t), (t, 2)) + t*Derivative(z(t), t) - t + z(t),0),Eq(t*Derivative(y(t), t) + z(t) - log(t),0)] 
ics = {} 
dsolve(ode,func=[y(t),z(t)],ics=ics)
 

KeyError : Derivative(z(t), t)