74.7.6 problem 6

Internal problem ID [16083]
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 : 6
Date solved : Tuesday, January 28, 2025 at 08:38:33 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+3 y&=\sqrt {y}\, \sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(t),t)+3*y(t)=sqrt(y(t))*sin(t),y(t), singsol=all)
 

\[ \sqrt {y}+\frac {2 \cos \left (t \right )}{13}-\frac {3 \sin \left (t \right )}{13}-{\mathrm e}^{-\frac {3 t}{2}} c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 40

DSolve[D[y[t],t]+3*y[t]==Sqrt[y[t]]*Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} e^{-3 t} \left (\int _1^te^{\frac {3 K[1]}{2}} \sin (K[1])dK[1]+2 c_1\right ){}^2 \]