47.1.13 problem 13

Internal problem ID [7394]
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
Date solved : Monday, January 27, 2025 at 02:51:57 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 x^{2}+4 x +2}{2 y-2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.460 (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)
 

\[ y = 1-\sqrt {\left (x +2\right ) \left (x^{2}+2\right )} \]

✓ Solution by Mathematica

Time used: 0.144 (sec). Leaf size: 26

DSolve[{D[y[x],x]==(3*x^2+4*x+2)/(2*(y[x]-1)),{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 1-\sqrt {x^3+2 x^2+2 x+4} \]