Internal problem ID [14377]
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: 34.
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: 0.062 (sec). Leaf size: 44
dsolve([diff(y(t),t)-2*y(t)=t^2*sqrt(y(t)),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = 1+4 \,{\mathrm e}^{2 t}+2 \left (-t^{2}-2 t -2\right ) {\mathrm e}^{t}+\frac {t^{4}}{4}+t^{3}+2 t^{2}+2 t \]
✓ Solution by Mathematica
Time used: 0.164 (sec). Leaf size: 42
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-4 e^t+2\right )^2 \\ y(t)\to \frac {1}{4} \left (t^2+2 t+2\right )^2 \\ \end{align*}