44.5.36 problem 36

Internal problem ID [7098]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 36
Date solved : Tuesday, February 04, 2025 at 12:14:20 AM
CAS classification : [_separable]

\begin{align*} \left (2 y-2\right ) y^{\prime }&=3 x^{2}+4 x +2 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 19

dsolve([(2*y(x)-2)*diff(y(x),x)=3*x^2+4*x+2,y(1) = -2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.279 (sec). Leaf size: 26

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

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