48.1.3 problem Example 3.3

Internal problem ID [7504]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page 114
Problem number : Example 3.3
Date solved : Monday, January 27, 2025 at 03:02:50 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: 0.018 (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: 0.146 (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]
 

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