44.5.80 problem 67 (a)

Internal problem ID [7142]
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 : 67 (a)
Date solved : Tuesday, February 04, 2025 at 12:38:32 AM
CAS classification : [_separable]

\begin{align*} \left (2 y+2\right ) y^{\prime }-4 x^{3}-6 x&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 20

dsolve([(2*y(x)+2)*diff(y(x),x)-(4*x^3+6*x)=0,y(0) = -3],y(x), singsol=all)
 

\[ y = -1-\sqrt {x^{4}+3 x^{2}+4} \]

✓ Solution by Mathematica

Time used: 0.131 (sec). Leaf size: 23

DSolve[{(2*y[x]+2)*D[y[x],x]-(4*x^3+6*x)==0,{y[0]==-3}},y[x],x,IncludeSingularSolutions -> True]
 

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