72.7.16 problem 16

Internal problem ID [14757]
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 : Tuesday, January 28, 2025 at 07:13:57 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 54

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

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

✓ Solution by Mathematica

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

DSolve[D[y[t],t]==y[t]+4*Cos[t^2],y[t],t,IncludeSingularSolutions -> True]
 

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