Internal problem ID [14217]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 57 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\sqrt {y}\, \cos \left (t \right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.484 (sec). Leaf size: 12
dsolve([diff(y(t),t)=sqrt(y(t))*cos(t),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\sin \left (t \right )+2\right )^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 29
DSolve[{y'[t]==Sqrt[y[t]]*Cos[t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} (\sin (t)-2)^2 \\ y(t)\to \frac {1}{4} (\sin (t)+2)^2 \\ \end{align*}