14.6.1 problem 5 (d)

Internal problem ID [2543]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.1. Algebraic properties of solutions. Excercises page 136
Problem number : 5 (d)
Date solved : Monday, January 27, 2025 at 05:59:52 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 9

dsolve([2*t^2*diff(y(t),t$2)+3*t*diff(y(t),t)-y(t)=0,y(1) = 2, D(y)(1) = 1],y(t), singsol=all)
 

\[ y = 2 \sqrt {t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 12

DSolve[{2*t^2*D[y[t],{t,2}]+3*t*D[y[t],t]-y[t]==0,{y[1]==2,Derivative[1][y][1] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 \sqrt {t} \]