Internal problem ID [14325]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{2}+\left (1+2 t y\right ) y^{\prime }=2 \sin \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.312 (sec). Leaf size: 25
dsolve([(y(t)^2-2*sin(2*t))+(1+2*t*y(t))*diff(y(t),t)=0,y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {-1+\sqrt {-4 t \cos \left (2 t \right )+8 t +1}}{2 t} \]
✓ Solution by Mathematica
Time used: 1.457 (sec). Leaf size: 30
DSolve[{(y[t]^2-2*Sin[2*t])+(1+2*t*y[t])*y'[t]==0,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\sqrt {8 t-4 t \cos (2 t)+1}-1}{2 t} \]