Internal problem ID [4973]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 x^{2}+4 x +2}{2 y-2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 19
dsolve([diff(y(x),x)=(3*x^2+4*x+2)/(2*(y(x)-1)),y(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = 1-\sqrt {\left (x +2\right ) \left (x^{2}+2\right )} \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 22
DSolve[{y'[x]==(3*x^2+4*x+2)/(2*(y[x]-1)),{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1-\sqrt {(x+2) \left (x^2+2\right )} \\ \end{align*}