72.7.16 problem 16

Internal problem ID [14686]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 16
Date solved : Monday, March 31, 2025 at 12:52:59 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=y+4 \cos \left (t^{2}\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 54

ode:=diff(y(t),t) = y(t)+4*cos(t^2); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (\frac {1}{4}-\frac {i}{4}\right ) {\mathrm e}^{t} \sqrt {2}\, \left (2 \,{\mathrm e}^{-\frac {i}{4}} \operatorname {erf}\left (\frac {\left (1-i+\left (2+2 i\right ) t \right ) \sqrt {2}}{4}\right ) \sqrt {\pi }+2 i \sqrt {\pi }\, {\mathrm e}^{\frac {i}{4}} \operatorname {erf}\left (\left (\frac {1}{4}-\frac {i}{4}\right ) \sqrt {2}\, \left (2 t +i\right )\right )+\left (1+i\right ) c_1 \sqrt {2}\right ) \]

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 32

ode=D[y[t],t]==y[t]+4*Cos[t^2]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^t \left (\int _1^t4 e^{-K[1]} \cos \left (K[1]^2\right )dK[1]+c_1\right ) \]

✓ Sympy. Time used: 3.993 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t) - 4*cos(t**2) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ - \int y{\left (t \right )} e^{- t}\, dt - 4 \int e^{- t} \cos {\left (t^{2} \right )}\, dt = C_{1} \]