Internal problem ID [14376]
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: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }+2 y-t^{2} \sqrt {y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 16
dsolve([diff(y(t),t)+2*y(t)=t^2*sqrt(y(t)),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (t^{2}-2 t +2\right )^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 48
DSolve[{y'[t]+2*y[t]==t^2*Sqrt[y[t]],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} \left (t^2-2 t+2\right )^2 \\ y(t)\to \frac {1}{4} e^{-2 t} \left (e^t \left (t^2-2 t+2\right )-4\right )^2 \\ \end{align*}