Internal problem ID [14348]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-2 y-\frac {\cos \left (t \right )}{\sqrt {y}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(t),t)-2*y(t)=y(t)^(-1/2)*cos(t),y(t), singsol=all)
\[ y \left (t \right )^{\frac {3}{2}}+\frac {9 \cos \left (t \right )}{20}-\frac {3 \sin \left (t \right )}{20}-c_{1} {\mathrm e}^{3 t} = 0 \]
✓ Solution by Mathematica
Time used: 3.757 (sec). Leaf size: 40
DSolve[y'[t]-2*y[t]==y[t]^(-1/2)*Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\left (\frac {3 \sin (t)}{5}-\frac {9 \cos (t)}{5}+4 c_1 e^{3 t}\right ){}^{2/3}}{2 \sqrt [3]{2}} \]