74.7.33 problem 33

Internal problem ID [16039]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 33
Date solved : Monday, March 31, 2025 at 02:34:08 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+2 y&=t^{2} \sqrt {y} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.092 (sec). Leaf size: 16

ode:=diff(y(t),t)+2*y(t) = t^2*y(t)^(1/2); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {\left (t^{2}-2 t +2\right )^{2}}{4} \]

✓ Mathematica. Time used: 0.182 (sec). Leaf size: 48

ode=D[y[t],t]+2*y[t]==t^2*Sqrt[y[t]]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \frac {1}{4} \left (t^2-2 t+2\right )^2 \\ y(t)\to \frac {1}{4} e^{-2 t} \left (e^t \left (t^2-2 t+2\right )-4\right )^2 \\ \end{align*}

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants