74.7.5 problem 5

Internal problem ID [16082]
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 : 5
Date solved : Tuesday, January 28, 2025 at 08:38:14 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }-2 y&=\frac {\cos \left (t \right )}{\sqrt {y}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(t),t)-2*y(t)=y(t)^(-1/2)*cos(t),y(t), singsol=all)
 

\[ y^{{3}/{2}}+\frac {9 \cos \left (t \right )}{20}-\frac {3 \sin \left (t \right )}{20}-c_{1} {\mathrm e}^{3 t} = 0 \]

✓ Solution by Mathematica

Time used: 9.402 (sec). Leaf size: 45

DSolve[D[y[t],t]-2*y[t]==y[t]^(-1/2)*Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

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