84.1.2 problem 1.2

Internal problem ID [22066]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 1. Basic concepts
Problem number : 1.2
Date solved : Thursday, October 02, 2025 at 08:23:21 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} t y^{\prime \prime }+t^{2} y^{\prime }-\sin \left (t \right ) \sqrt {t}&=t^{2}-t +1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 45

ode:=t*diff(diff(y(t),t),t)+t^2*diff(y(t),t)-sin(t)*t^(1/2) = t^2-t+1; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \int \left (\int \frac {\left (t \sin \left (t \right )+t^{{5}/{2}}-t^{{3}/{2}}+\sqrt {t}\right ) {\mathrm e}^{\frac {t^{2}}{2}}}{t^{{3}/{2}}}d t +c_1 \right ) {\mathrm e}^{-\frac {t^{2}}{2}}d t +c_2 \]

✓ Mathematica. Time used: 62.516 (sec). Leaf size: 72

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

\begin{align*} y(t)&\to \int _1^te^{-\frac {1}{2} K[2]^2} \left (c_1+\int _1^{K[2]}\frac {e^{\frac {K[1]^2}{2}} \left (K[1]^2-K[1]+\sin (K[1]) \sqrt {K[1]}+1\right )}{K[1]}dK[1]\right )dK[2]+c_2 \end{align*}

✗ Sympy

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

Timed Out